A? dori ?i eu dou? formule pentru a calcula urm?toarele sume:
A=1/1X2+1/3X4+...+1/99X100
B=1/51+1/52+..1/100

Pentru A trebuie sa fie o formula foarte delicata, care sa reproduca numarul urmator calculat cu fierul de calculat:

sage: termeni = [ 1/ (2*k+1) / (2*k+2) for k in [0..49] ]

sage: termeni
[1/2, 1/12, 1/30, 1/56, 1/90, 1/132, 1/182, 1/240, 1/306, 1/380, 1/462, 1/552, 1/650, 1/756, 1/870, 1/992, 1/1122, 1/1260, 1/1406, 1/1560, 1/1722, 1/1892, 1/2070, 1/2256, 1/2450, 1/2652, 1/2862, 1/3080, 1/3306, 1/3540, 1/3782, 1/4032, 1/4290, 1/4556, 1/4830, 1/5112, 1/5402, 1/5700, 1/6006, 1/6320, 1/6642, 1/6972, 1/7310, 1/7656, 1/8010, 1/8372, 1/8742, 1/9120, 1/9506, 1/9900]

sage: sum( termeni )
47979622564155786918478609039662898122617 / 69720375229712477164533808935312303556800
sage:

Pentru B avem o suma armonica. Se stie ca nnu se stie o formula (exacta)...

sage: sum( [ 1/k for k in [51..100] ] )
47979622564155786918478609039662898122617 / 69720375229712477164533808935312303556800

[Citat] A? dori ?i eu dou? formule pentru a calcula urm?toarele sume: A=1/1X2+1/3X4+...+1/99X100 B=1/51+1/52+..1/100