Question

CTR:

1+2+2²+2³+...+2⁵⁰⁰⁶ chi hết cho 7

Answer 1

A=(1+2+2^2)+...+2^5004(1+2+2^2)

=7(1+...+2^5004) chia hết cho 7

Answer 2

Ta có: 1+2+2²+2³+...+2⁵⁰⁰⁶

= ( 1+2+2²)+( 2³+2⁴+2⁵)+...+( 2⁵⁰⁰⁴+2⁵⁰⁰⁵+2⁵⁰⁰⁶)

= ( 1+2+2²)+2³.(1+2+2² )+...+ 2⁵⁰⁰⁴.(1+2+2²)

= 1.7+2³.7 + ... + 2⁵⁰⁰⁴.7

= 7 . ( 1+...+ 2⁵⁰⁰⁴) chia hết cho 7 

=> 1+2+2²+2³+...+2⁵⁰⁰⁶ chia hết cho 7 ( dcpcm)