Question

A=7^1+7^2+7^3+...+7^2010

Tính tổng

 

Answer 1

Ta có:A=7+7²+7³+...+7²⁰¹⁰

=>7A=7(7+7²+7³+...+7²⁰¹⁰⁾

7A=49+7³+7⁴+...+7²⁰¹¹

=>7A-A=(49+7³+7⁴+...+7²⁰¹¹)-(7+7²+7³+...+7²⁰¹⁰)

=>6A=7²⁰¹¹-7

=>A=(7²⁰¹¹-7):6

Vậy A=(7²⁰¹¹-7):6

Answer 2

A=7^1+7^2+...7^2010

7×A=7^2+7^3+.....7^2011

7×A-A=(7^2+7^3+...+7^2011)-(7^1+7^2+....+7^2010)

=7^2011-7^1