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Fie Q(x) catul impartirii polinomului
Valoarea Q(1) este...
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Verificare cu calculatorul:
sage: f = 99*(x^101-1)-101*x*(x^99-1)
sage: ( f / (x-1)^3 ) . simplify_rational()
99*x^98 + 196*x^97 + 291*x^96 + 384*x^95 + 475*x^94 + 564*x^93 + 651*x^92 + 736*x^91 + 819*x^90 + 900*x^89 + 979*x^88 + 1056*x^87 + 1131*x^86 + 1204*x^85 + 1275*x^84 + 1344*x^83 + 1411*x^82 + 1476*x^81 + 1539*x^80 + 1600*x^79 + 1659*x^78 + 1716*x^77 + 1771*x^76 + 1824*x^75 + 1875*x^74 + 1924*x^73 + 1971*x^72 + 2016*x^71 + 2059*x^70 + 2100*x^69 + 2139*x^68 + 2176*x^67 + 2211*x^66 + 2244*x^65 + 2275*x^64 + 2304*x^63 + 2331*x^62 + 2356*x^61 + 2379*x^60 + 2400*x^59 + 2419*x^58 + 2436*x^57 + 2451*x^56 + 2464*x^55 + 2475*x^54 + 2484*x^53 + 2491*x^52 + 2496*x^51 + 2499*x^50 + 2500*x^49 + 2499*x^48 + 2496*x^47 + 2491*x^46 + 2484*x^45 + 2475*x^44 + 2464*x^43 + 2451*x^42 + 2436*x^41 + 2419*x^40 + 2400*x^39 + 2379*x^38 + 2356*x^37 + 2331*x^36 + 2304*x^35 + 2275*x^34 + 2244*x^33 + 2211*x^32 + 2176*x^31 + 2139*x^30 + 2100*x^29 + 2059*x^28 + 2016*x^27 + 1971*x^26 + 1924*x^25 + 1875*x^24 + 1824*x^23 + 1771*x^22 + 1716*x^21 + 1659*x^20 + 1600*x^19 + 1539*x^18 + 1476*x^17 + 1411*x^16 + 1344*x^15 + 1275*x^14 + 1204*x^13 + 1131*x^12 + 1056*x^11 + 979*x^10 + 900*x^9 + 819*x^8 + 736*x^7 + 651*x^6 + 564*x^5 + 475*x^4 + 384*x^3 + 291*x^2 + 196*x + 99
sage: f.limit(x=1)
0
sage: ( f / (x-1)^3 ) . limit( x=1 )
166650
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df (gauss)
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Multumesc.
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