Question

7+7^2+7^3+...+7^87 ATENTIE: ^ INSEAMNA LA PUTEREA

Answer 1

Salut,

Notăm cu S suma din enunţ:

$S=7+7^2+7^3+\ldots+7^{86}+7^{87}.$

Calculăm 7*S:

$7\cdot S=7^2+7^3+7^4+\ldots+7^{87}+7^{88}.$

Efectuăm 7S-S=6S:

$6\cdot S=\cancel{7^2}+\cancel{7^3}+\cancel{7^4}+\ldots+\cancel{7^{87}}+7^{88}-(7+\cancel{7^2}+\cancel{7^3}+\cancel{7^4}+\ldots+\cancel{7^{87}})=7^{88}-7=7\cdot(7^{87}-1),\;deci\;S=\dfrac{7\cdot(7^{87}-1)}{6}.$

Green eyes.