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Mesaj |
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Buna seara,
Se da triunghiul ABC cu centrul sau de greutate G.Notam
razele cercurilor inscrise respectiv circumscrise triunghiurilor GBC,GAC si GAB.Trebuie sa arat ca
Cum pot face asta?
Multumesc
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[Citat]
Buna seara,
Se da triunghiul ABC cu centrul sau de greutate G.Notam
razele cercurilor inscrise respectiv circumscrise triunghiurilor GBC,GAC si GAB.Trebuie sa arat ca
Cum pot face asta?
Multumesc |
Buna!
E tarziu si trebuie sa ma culc instantaneu, uneori e greu, dar de aceea nu pot tipari pe larg...
Ne uitam la triunghiurile ABC si GBC. Desigur ca
S( ABC ) = 3 S( GBC ) .
(Am notat cu S( ? ) aria lui ? .)
Apoi ne uitam la laturile lui GBC.
GB este 2/3 din mediana din B a lui ABC,
GC este 2/3 din mediana din C a lui ABC,
BC este BC si in ABC,
cele trei lucruri se regasesc (dupa impartire fortata cu 3 in numitor si pus 3-ul altundeva incat sa avem egalitate)
in numitorul urat de mai sus.
Ramana sa mai stim ca intr-un triunghi MNP, daca marcam cu I centrul cercului inscris,
scriind
S( MNP ) = S( MNI ) + S( NPI ) + S( PMI )
si scriind in membrul drept aria ca (1/2) din inaltimea "r" inmultita cu latura opusa...
Mai sunt intrebari?! (Daca da, rog a se pune fara retineri!)
---
df (gauss)
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Am inteles.Am calculat
si membrul drept si am ajuns la egalitate.Multumesc foarte mult!
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Nu stiu daca ar trebui sa postez aici,dar as mai avea o intrebare legata de alta problema.As vrea sa imi oferiti doar un indiciu .
Cum pot calcula partea intreaga a acestei sume :
?
|
|
|
Nu stiu daca ar trebui sa postez aici,dar as mai avea o intrebare legata de alta problema.As vrea sa imi oferiti doar un indiciu .
Cum pot calcula partea intreaga a acestei sume :
?
|
|
|
[Citat]
Nu stiu daca ar trebui sa postez aici, as mai avea o intrebare legata de alta problema. As vrea sa imi oferiti doar un indiciu .
Cum pot calcula partea intreaga a acestei sume :
? |
Problema a mai aparut acum cateva zile (asa sau foarte asemanator) pe site,
domnul Enescu a dat o indicatie, nu gasesc locul asa ca mi-e mai usor sa scriu cum m-as apuca eu de ea.
In primul rand sunt acasa, nu in conditii de concurs, asa ca dau imediat drumul la computer pentru a gasi valoarea primilor cativa sumanzi si a sumelor corespunzatoare, cod PARI/GP:
? for( k=1,99, termen=1/(k+1)/sqrt(k); suma = suma+termen; print( "k=",k, " termen = ", termen, " suma = ", suma ) )
k=1 termen = 0.5000000000000000000000000000 suma = 0.5000000000000000000000000000
k=2 termen = 0.2357022603955158414669481207 suma = 0.7357022603955158414669481207
k=3 termen = 0.1443375672974064411272871951 suma = 0.8800398276929222825942353158
k=4 termen = 0.1000000000000000000000000000 suma = 0.9800398276929222825942353158
k=5 termen = 0.07453559924999298988030578896 suma = 1.054575426942915272474541105
apoi mai vin o sumedenie de informatii pe drum
k=6 termen = 0.05832118435198043090945914464 suma = 1.112896611294895703384000249
k=7 termen = 0.04724555912615340340181456703 suma = 1.160142170421049106785814816
k=8 termen = 0.03928371006591930691115802012 suma = 1.199425880486968413696972837
k=9 termen = 0.03333333333333333333333333333 suma = 1.232759213820301747030306170
k=10 termen = 0.02874797872880344847271721404 suma = 1.261507192549105195503023384
k=11 termen = 0.02512594538148030188723433891 suma = 1.286633137930585497390257723
k=12 termen = 0.02220577958421637555804418387 suma = 1.308838917514801872948301907
k=13 termen = 0.01981072129375818292922649048 suma = 1.328649638808560055877528397
k=14 termen = 0.01781741612749495897897023206 suma = 1.346467054936055014856498629
k=15 termen = 0.01613743060919757035491360583 suma = 1.362604485545252585211412235
k=16 termen = 0.01470588235294117647058823529 suma = 1.377310367898193761682000470
k=17 termen = 0.01347420139090738741771702567 suma = 1.390784569289101149099717496
k=18 termen = 0.01240538212607978112983937477 suma = 1.403189951415180930229556871
k=19 termen = 0.01147078669352808829536047891 suma = 1.414660738108709018524917350
k=20 termen = 0.01064794274999899855432939842 suma = 1.425308680858708017079246748
k=21 termen = 0.009918995010726926421186249337 suma = 1.435227675869434943500432997
k=22 termen = 0.009269596363287410186888597062 suma = 1.444497272232722353687321594
k=23 termen = 0.008688100585711448444922895044 suma = 1.453185372818433802132244489
k=24 termen = 0.008164965809277260327324280249 suma = 1.461350338627711062459568770
k=25 termen = 0.007692307692307692307692307692 suma = 1.469042646320018754767261077
k=26 termen = 0.007263560560673482663857869101 suma = 1.476306206880692237431118946
k=27 termen = 0.006873217490352687672727961673 suma = 1.483179424371044925103846908
k=28 termen = 0.006516628844986676331284767866 suma = 1.489696053216031601435131676
k=29 termen = 0.006189844605901728771552540795 suma = 1.495885897821933330206684217
k=30 termen = 0.005889489865646947456526556804 suma = 1.501775387687580277663210773
k=31 termen = 0.005612665688336715647297854132 suma = 1.507388053375916993310508628
k=32 termen = 0.005356869554443541851521548198 suma = 1.512744922930360535162030176
k=33 termen = 0.005119931057520524652273272253 suma = 1.517864853987881059814303448
k=34 termen = 0.004899959575500252496532901578 suma = 1.522764813563381312310836350
k=35 termen = 0.004695301415158425430608990708 suma = 1.527460114978539737741445340
k=36 termen = 0.004504504504504504504504504505 suma = 1.531964619483044242245949845
k=37 termen = 0.004326289139614665497154825210 suma = 1.536290908622658907743104670
k=38 termen = 0.004159523618737500978576378125 suma = 1.540450432241396408721681048
k=39 termen = 0.004003203845127178337081341744 suma = 1.544453636086523587058762390
k=40 termen = 0.003856436170937047965852309201 suma = 1.548310072257460635024614699
k=41 termen = 0.003718422902109668226764354050 suma = 1.552028495159570303251379053
k=42 termen = 0.003588449999118416517699871227 suma = 1.555616945158688719769078924
k=43 termen = 0.003465876598468287871217817124 suma = 1.559082821757157007640296741
k=44 termen = 0.003350126050864040251631245189 suma = 1.562432947808021047891927987
k=45 termen = 0.003240678228260564777404599520 suma = 1.565673626036281612669332586
k=46 termen = 0.003137062896912704967189896543 suma = 1.568810688933194317636522483
k=47 termen = 0.003038853989539469913535404011 suma = 1.571849542922733787550057887
k=48 termen = 0.002945664638722580431169126431 suma = 1.574795207561456367981227013
k=49 termen = 0.002857142857142857142857142857 suma = 1.577652350418599225124084156
k=50 termen = 0.002772967769359009899611154361 suma = 1.580425318187958235023695310
k=51 termen = 0.002692846315438480391402488617 suma = 1.583118164503396715415097799
k=52 termen = 0.002616510359552967556690291196 suma = 1.585734674862949682971788090
k=53 termen = 0.002543714147197944888573480954 suma = 1.588278389010147627860361571
k=54 termen = 0.002474232063417351614340690985 suma = 1.590752621073564979474702262
k=55 termen = 0.002407856651654436022308895273 suma = 1.593160477725219415497011157
k=56 termen = 0.002344396858880915655127662113 suma = 1.595504874584100331152138819
k=57 termen = 0.002283676477698351390573709863 suma = 1.597788551061798682542712529
k=58 termen = 0.002225532760334280621175163947 suma = 1.600014083822132963163887693
k=59 termen = 0.002169815183013731123098781645 suma = 1.602183899005146694286986475
k=60 termen = 0.002116384342189845292447686011 suma = 1.604300283347336539579434161
k=61 termen = 0.002065110966659612478617060480 suma = 1.606365394313996152058051221
k=62 termen = 0.002015875031749055560595246915 suma = 1.608381269345745207618646468
k=63 termen = 0.001968564963589725141742273626 suma = 1.610349834309334932760388742
k=64 termen = 0.001923076923076923076923076923 suma = 1.612272911232411855837311819
k=65 termen = 0.001879314160442552366519024063 suma = 1.614152225392854408203830843
k=66 termen = 0.001837186432527354219914039703 suma = 1.615989411825381762423744882
k=67 termen = 0.001796609475828017991649188702 suma = 1.617786021301209780415394071
k=68 termen = 0.001757504529248789663180481610 suma = 1.619543525830458570078574553
k=69 termen = 0.001719797901225274296601296635 suma = 1.621263323731683844375175849
k=70 termen = 0.001683420576527314985871573493 suma = 1.622946744308211159361047423
k=71 termen = 0.001648307858602574067025457728 suma = 1.624595052166813733428072880
k=72 termen = 0.001614399043804903023746220005 suma = 1.626209451210618636451819100
k=73 termen = 0.001581637124272034647884422126 suma = 1.627791088334890671099703522
k=74 termen = 0.001549968516584257075987292529 suma = 1.629341056851474928175690815
k=75 termen = 0.001519342813656909906603023107 suma = 1.630860399665131838082293838
k=76 termen = 0.001489712557601050427968893364 suma = 1.632350112222732888510262731
k=77 termen = 0.001461033031533819856877520531 suma = 1.633811145254266708367140252
k=78 termen = 0.001433262068537462975456676846 suma = 1.635244407322804171342596929
k=79 termen = 0.001406359876157529881343582544 suma = 1.636650767198961701223940511
k=80 termen = 0.001380288874999870182968625721 suma = 1.638031056073961571406909137
k=81 termen = 0.001355013550135501355013550136 suma = 1.639386069624097072761922687
k=82 termen = 0.001330500314154777641283251273 suma = 1.640716569938251850403205938
k=83 termen = 0.001306717380829646999705339372 suma = 1.642023287319081497402911278
k=84 termen = 0.001283634648447014007447632267 suma = 1.643306921967528511410358910
k=85 termen = 0.001261223591968931232558450654 suma = 1.644568145559497442642917361
k=86 termen = 0.001239457163257912824447529547 suma = 1.645807602722755355467364890
k=87 termen = 0.001218309698679312310025401717 suma = 1.647025912421434667777390292
k=88 termen = 0.001197756833458485585946279396 suma = 1.648223669254893153363336571
k=89 termen = 0.001177775422229288865333415777 suma = 1.649401444677122442228669987
k=90 termen = 0.001158343465263142612453807159 suma = 1.650559788142385584841123794
k=91 termen = 0.001139440039915128582360990905 suma = 1.651699228182300713423484785
k=92 termen = 0.001121045236865993347731986457 suma = 1.652820273419166706771216772
k=93 termen = 0.001103140100777048157831163469 suma = 1.653923413519943754929047935
k=94 termen = 0.001085706575009256218157769446 suma = 1.655009120094953011147205704
k=95 termen = 0.001068727450088702182767369868 suma = 1.656077847545041713329973074
k=96 termen = 0.001052186315628512928778902094 suma = 1.657130033860670226258751976
k=97 termen = 0.001036067515442468411713255987 suma = 1.658166101376112694670465232
k=98 termen = 0.001020356105608293686004104419 suma = 1.659186457481720988356469337
k=99 termen = 0.001005037815259212075489373557 suma = 1.660191495296980200431958710
?
Deci numarul dat intra intre 1 si 2, primii cativa termeni fac toata afacerea.
Indicatia pentru o solutie posibila este acum folosind sume Riemann.
Ce margini avem? Cod GP/PARI, cerem
f(x) = x^( -3/2 )
F(x) = -2 *x^( -1/2 )
f(2)
F(2)
f(4)
F(4)
f(100)
F(100)
intnum( x=4,100, f(x) )
F(100) - F(4)
intnum( x=2,[1], f(x) )
-F(2)
1/2 + 1/3/sqrt(2) + intnum( x=2,99, f(x) )
1/2 + 1/3/sqrt(2) + intnum( x=4,101, f(x) )
si dam de ? f(x) = x^( -3/2 )
? F(x) = -2 *x^( -1/2 )
? f(2)
%15 = 0.3535533905932737622004221811
? F(2)
%16 = -1.414213562373095048801688724
? f(4)
%17 = 0.1250000000000000000000000000
? F(4)
%18 = -1.000000000000000000000000000
? f(100)
%19 = 0.0009999999999999999999999999999
? F(100)
%20 = -0.2000000000000000000000000000
? intnum( x=4,100, f(x) )
%21 = 0.8000000000000000000000000000
? F(100) - F(4)
%22 = 0.8000000000000000000000000000
? intnum( x=2,[1], f(x) )
%23 = 1.414213562373095048722253574
? -F(2)
%24 = 1.414213562373095048801688724
? 1/2 + 1/3/sqrt(2) + intnum( x=2,99, f(x) )
%25 = 1.948908259716768475170762134
? 1/2 + 1/3/sqrt(2) + intnum( x=4,101, f(x) )
%26 = 1.536694822353518014333893370
---
df (gauss)
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[Citat]
[Citat]
Nu stiu daca ar trebui sa postez aici, as mai avea o intrebare legata de alta problema. As vrea sa imi oferiti doar un indiciu .
Cum pot calcula partea intreaga a acestei sume :
? |
Problema a mai aparut acum cateva zile (asa sau foarte asemanator) pe site,
domnul Enescu a dat o indicatie, nu gasesc locul asa ca mi-e mai usor sa scriu cum m-as apuca eu de ea.
In primul rand sunt acasa, nu in conditii de concurs, asa ca dau imediat drumul la computer pentru a gasi valoarea primilor cativa sumanzi si a sumelor corespunzatoare, cod PARI/GP:
? for( k=1,99, termen=1/(k+1)/sqrt(k); suma = suma+termen; print( "k=",k, " termen = ", termen, " suma = ", suma ) )
k=1 termen = 0.5000000000000000000000000000 suma = 0.5000000000000000000000000000
k=2 termen = 0.2357022603955158414669481207 suma = 0.7357022603955158414669481207
k=3 termen = 0.1443375672974064411272871951 suma = 0.8800398276929222825942353158
k=4 termen = 0.1000000000000000000000000000 suma = 0.9800398276929222825942353158
k=5 termen = 0.07453559924999298988030578896 suma = 1.054575426942915272474541105
apoi mai vin o sumedenie de informatii pe drum
k=6 termen = 0.05832118435198043090945914464 suma = 1.112896611294895703384000249
k=7 termen = 0.04724555912615340340181456703 suma = 1.160142170421049106785814816
k=8 termen = 0.03928371006591930691115802012 suma = 1.199425880486968413696972837
k=9 termen = 0.03333333333333333333333333333 suma = 1.232759213820301747030306170
k=10 termen = 0.02874797872880344847271721404 suma = 1.261507192549105195503023384
k=11 termen = 0.02512594538148030188723433891 suma = 1.286633137930585497390257723
k=12 termen = 0.02220577958421637555804418387 suma = 1.308838917514801872948301907
k=13 termen = 0.01981072129375818292922649048 suma = 1.328649638808560055877528397
k=14 termen = 0.01781741612749495897897023206 suma = 1.346467054936055014856498629
k=15 termen = 0.01613743060919757035491360583 suma = 1.362604485545252585211412235
k=16 termen = 0.01470588235294117647058823529 suma = 1.377310367898193761682000470
k=17 termen = 0.01347420139090738741771702567 suma = 1.390784569289101149099717496
k=18 termen = 0.01240538212607978112983937477 suma = 1.403189951415180930229556871
k=19 termen = 0.01147078669352808829536047891 suma = 1.414660738108709018524917350
k=20 termen = 0.01064794274999899855432939842 suma = 1.425308680858708017079246748
k=21 termen = 0.009918995010726926421186249337 suma = 1.435227675869434943500432997
k=22 termen = 0.009269596363287410186888597062 suma = 1.444497272232722353687321594
k=23 termen = 0.008688100585711448444922895044 suma = 1.453185372818433802132244489
k=24 termen = 0.008164965809277260327324280249 suma = 1.461350338627711062459568770
k=25 termen = 0.007692307692307692307692307692 suma = 1.469042646320018754767261077
k=26 termen = 0.007263560560673482663857869101 suma = 1.476306206880692237431118946
k=27 termen = 0.006873217490352687672727961673 suma = 1.483179424371044925103846908
k=28 termen = 0.006516628844986676331284767866 suma = 1.489696053216031601435131676
k=29 termen = 0.006189844605901728771552540795 suma = 1.495885897821933330206684217
k=30 termen = 0.005889489865646947456526556804 suma = 1.501775387687580277663210773
k=31 termen = 0.005612665688336715647297854132 suma = 1.507388053375916993310508628
k=32 termen = 0.005356869554443541851521548198 suma = 1.512744922930360535162030176
k=33 termen = 0.005119931057520524652273272253 suma = 1.517864853987881059814303448
k=34 termen = 0.004899959575500252496532901578 suma = 1.522764813563381312310836350
k=35 termen = 0.004695301415158425430608990708 suma = 1.527460114978539737741445340
k=36 termen = 0.004504504504504504504504504505 suma = 1.531964619483044242245949845
k=37 termen = 0.004326289139614665497154825210 suma = 1.536290908622658907743104670
k=38 termen = 0.004159523618737500978576378125 suma = 1.540450432241396408721681048
k=39 termen = 0.004003203845127178337081341744 suma = 1.544453636086523587058762390
k=40 termen = 0.003856436170937047965852309201 suma = 1.548310072257460635024614699
k=41 termen = 0.003718422902109668226764354050 suma = 1.552028495159570303251379053
k=42 termen = 0.003588449999118416517699871227 suma = 1.555616945158688719769078924
k=43 termen = 0.003465876598468287871217817124 suma = 1.559082821757157007640296741
k=44 termen = 0.003350126050864040251631245189 suma = 1.562432947808021047891927987
k=45 termen = 0.003240678228260564777404599520 suma = 1.565673626036281612669332586
k=46 termen = 0.003137062896912704967189896543 suma = 1.568810688933194317636522483
k=47 termen = 0.003038853989539469913535404011 suma = 1.571849542922733787550057887
k=48 termen = 0.002945664638722580431169126431 suma = 1.574795207561456367981227013
k=49 termen = 0.002857142857142857142857142857 suma = 1.577652350418599225124084156
k=50 termen = 0.002772967769359009899611154361 suma = 1.580425318187958235023695310
k=51 termen = 0.002692846315438480391402488617 suma = 1.583118164503396715415097799
k=52 termen = 0.002616510359552967556690291196 suma = 1.585734674862949682971788090
k=53 termen = 0.002543714147197944888573480954 suma = 1.588278389010147627860361571
k=54 termen = 0.002474232063417351614340690985 suma = 1.590752621073564979474702262
k=55 termen = 0.002407856651654436022308895273 suma = 1.593160477725219415497011157
k=56 termen = 0.002344396858880915655127662113 suma = 1.595504874584100331152138819
k=57 termen = 0.002283676477698351390573709863 suma = 1.597788551061798682542712529
k=58 termen = 0.002225532760334280621175163947 suma = 1.600014083822132963163887693
k=59 termen = 0.002169815183013731123098781645 suma = 1.602183899005146694286986475
k=60 termen = 0.002116384342189845292447686011 suma = 1.604300283347336539579434161
k=61 termen = 0.002065110966659612478617060480 suma = 1.606365394313996152058051221
k=62 termen = 0.002015875031749055560595246915 suma = 1.608381269345745207618646468
k=63 termen = 0.001968564963589725141742273626 suma = 1.610349834309334932760388742
k=64 termen = 0.001923076923076923076923076923 suma = 1.612272911232411855837311819
k=65 termen = 0.001879314160442552366519024063 suma = 1.614152225392854408203830843
k=66 termen = 0.001837186432527354219914039703 suma = 1.615989411825381762423744882
k=67 termen = 0.001796609475828017991649188702 suma = 1.617786021301209780415394071
k=68 termen = 0.001757504529248789663180481610 suma = 1.619543525830458570078574553
k=69 termen = 0.001719797901225274296601296635 suma = 1.621263323731683844375175849
k=70 termen = 0.001683420576527314985871573493 suma = 1.622946744308211159361047423
k=71 termen = 0.001648307858602574067025457728 suma = 1.624595052166813733428072880
k=72 termen = 0.001614399043804903023746220005 suma = 1.626209451210618636451819100
k=73 termen = 0.001581637124272034647884422126 suma = 1.627791088334890671099703522
k=74 termen = 0.001549968516584257075987292529 suma = 1.629341056851474928175690815
k=75 termen = 0.001519342813656909906603023107 suma = 1.630860399665131838082293838
k=76 termen = 0.001489712557601050427968893364 suma = 1.632350112222732888510262731
k=77 termen = 0.001461033031533819856877520531 suma = 1.633811145254266708367140252
k=78 termen = 0.001433262068537462975456676846 suma = 1.635244407322804171342596929
k=79 termen = 0.001406359876157529881343582544 suma = 1.636650767198961701223940511
k=80 termen = 0.001380288874999870182968625721 suma = 1.638031056073961571406909137
k=81 termen = 0.001355013550135501355013550136 suma = 1.639386069624097072761922687
k=82 termen = 0.001330500314154777641283251273 suma = 1.640716569938251850403205938
k=83 termen = 0.001306717380829646999705339372 suma = 1.642023287319081497402911278
k=84 termen = 0.001283634648447014007447632267 suma = 1.643306921967528511410358910
k=85 termen = 0.001261223591968931232558450654 suma = 1.644568145559497442642917361
k=86 termen = 0.001239457163257912824447529547 suma = 1.645807602722755355467364890
k=87 termen = 0.001218309698679312310025401717 suma = 1.647025912421434667777390292
k=88 termen = 0.001197756833458485585946279396 suma = 1.648223669254893153363336571
k=89 termen = 0.001177775422229288865333415777 suma = 1.649401444677122442228669987
k=90 termen = 0.001158343465263142612453807159 suma = 1.650559788142385584841123794
k=91 termen = 0.001139440039915128582360990905 suma = 1.651699228182300713423484785
k=92 termen = 0.001121045236865993347731986457 suma = 1.652820273419166706771216772
k=93 termen = 0.001103140100777048157831163469 suma = 1.653923413519943754929047935
k=94 termen = 0.001085706575009256218157769446 suma = 1.655009120094953011147205704
k=95 termen = 0.001068727450088702182767369868 suma = 1.656077847545041713329973074
k=96 termen = 0.001052186315628512928778902094 suma = 1.657130033860670226258751976
k=97 termen = 0.001036067515442468411713255987 suma = 1.658166101376112694670465232
k=98 termen = 0.001020356105608293686004104419 suma = 1.659186457481720988356469337
k=99 termen = 0.001005037815259212075489373557 suma = 1.660191495296980200431958710
?
Deci numarul dat intra intre 1 si 2, primii cativa termeni fac toata afacerea.
Indicatia pentru o solutie posibila este acum folosind sume Riemann.
Ce margini avem? Cod GP/PARI, cerem
f(x) = x^( -3/2 )
F(x) = -2 *x^( -1/2 )
f(2)
F(2)
f(4)
F(4)
f(100)
F(100)
intnum( x=4,100, f(x) )
F(100) - F(4)
intnum( x=2,[1], f(x) )
-F(2)
1/2 + 1/3/sqrt(2) + intnum( x=2,99, f(x) )
1/2 + 1/3/sqrt(2) + intnum( x=4,101, f(x) )
si dam de
? f(x) = x^( -3/2 )
? F(x) = -2 *x^( -1/2 )
? f(2)
%15 = 0.3535533905932737622004221811
? F(2)
%16 = -1.414213562373095048801688724
? f(4)
%17 = 0.1250000000000000000000000000
? F(4)
%18 = -1.000000000000000000000000000
? f(100)
%19 = 0.0009999999999999999999999999999
? F(100)
%20 = -0.2000000000000000000000000000
? intnum( x=4,100, f(x) )
%21 = 0.8000000000000000000000000000
? F(100) - F(4)
%22 = 0.8000000000000000000000000000
? intnum( x=2,[1], f(x) )
%23 = 1.414213562373095048722253574
? -F(2)
%24 = 1.414213562373095048801688724
? 1/2 + 1/3/sqrt(2) + intnum( x=2,99, f(x) )
%25 = 1.948908259716768475170762134
? 1/2 + 1/3/sqrt(2) + intnum( x=4,101, f(x) )
%26 = 1.536694822353518014333893370
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Acum am vazut postul cu aceeasi problema.Ideea cu incadrarea sumei intre doua numere-asta am inteles,dar ma tem ca nu inteleg rezolvarea,restul...
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[Citat]
Nu stiu daca ar trebui sa postez aici, as mai avea o intrebare legata de alta problema. As vrea sa imi oferiti doar un indiciu .
Cum pot calcula partea intreaga a acestei sume :
?
<........................................................................>
Acum am vazut postul cu aceeasi problema.
Ideea cu incadrarea sumei intre doua numere - asta am inteles,
dar ma tem ca nu inteleg rezolvarea, restul... |
Este vina mea atunci, intotdeauna am incercat sa dau solutia care face cat de mult cat mai la limita. In cazul de fata ni se cere sa aratam ca un numar este intre 1 si 2. Iata un drum scurt. (Un drum care nu arata insa ce sa facem in cazuri asemanatoare mai stranse si care este mesterit, nu in sensul metodelor standard ale analizei matematice in astfel de situatii.)
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df (gauss)
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Pentru S > 1 folosisem inegalitatea
Dar calculand imi dadea 99/100 = 0,99 si nu as fi putut spune care este partea intreaga.Stiu ca suna stupid intrebarea mea,dar cum de ati ales 3/2 pentru fractia a doua si 7/4 pentru a treia?...
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[Citat]
Pentru S > 1 folosisem inegalitatea
Dar calculand imi dadea 99/100 = 0,99 si nu as fi putut spune care este partea intreaga.Stiu ca suna stupid intrebarea mea,dar cum de ati ales 3/2 pentru fractia a doua si 7/4 pentru a treia?... |
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Intr-adevar,era atat de simplu.Multumesc !
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