Question

chứng minh tổng sau

a) A=2+2^2+2^3 +.........+2^59+2^60

                         chia hết cho 7

Answer 1

2+2^2+2^3+...+2^60

=(2+2^2+2^30)+...+(2^58+2^59+2^60)

=2*(1+2+2^2)+...+2^58*(1+2+2^2)

=2*7+...+2^58*7

=(2+...+2^58)*7

Suy ra ĐPCM

Answer 2

A=2+2²+2³+...+2⁶⁰

=(2+2²+2³)+...+(2⁵⁸+2⁵⁹+2⁶⁰)

=2.(1+2+2²)+...+2⁵⁸.(1+2+2²)

=2.7+...+2⁵⁸.7

=7.(2+...+2⁵⁸) chia hết cho 7