Question

tính tổng :A= 1+7+7^2+7^3+....+7^2016

 

Answer 1

\(A=1+7+7^2+7^3+...+7^{2016}\)

\(7A=7\left(1+7+7^2+...+7^{2016}\right)\)

\(7A=7+7^2+7^3+...+7^{2017}\)

\(6A=7A-A=7+7^2+7^3+...+7^{2017}-1-7-7^2-...-7^{2016}\)

\(6A=7^{2017}-7\)

\(A=\left(\frac{7^{2017}-7}{6}\right)\)

Answer 2

\(\left(\frac{7^{2017}-7}{6}\right)\)

Answer 3

A= 1+7+7²+7³+....+7²⁰¹⁶

7A=7(1+7+7²+...+7²⁰¹⁶)

7A=7+7²+7³+...+7²⁰¹⁷

6A=7A−A=7+7²+7³+...+7²⁰¹⁷−1−7−7²−...−7²⁰¹⁶

6A=7²⁰¹⁷−7

A=(7²⁰¹⁷−7) / 6