Question

Cho A=2⁰+2¹+2²+2³+...+2²⁰⁰⁹+2²⁰¹⁰. Tìm số dư khi chia cho 7

Answer 1

A =1+ (2+2²+2³) + ( 2⁴+2⁵+2⁶ ) + .....+ ( 2²⁰⁰⁸ +2²⁰⁰⁹+2²⁰¹⁰)  = 1+ 7 .( 2+2⁴ + 2⁷ +.....+ 2²⁰⁰⁸)

=> A chia 7 dư 1

Answer 2

ta co : 

A=2⁰+2¹+2²+...2²⁰⁰⁹+2²⁰¹⁰

=>A=(2⁰+2¹+2²)+...+(2²⁰⁰⁸+2²⁰⁰⁹+2²⁰¹⁰)

=>A=(2^0+2^1+2^2)+...+2^2008.(2^0+2^1+2^2)

=>A=(1+...+2^2008).7 chia het cho 7 

=>A chia het cho 7 

=>A chia het cho 7 du 0

**** nhe