Question

Cho tổng S=1+2+2²+2³+...+2⁵⁹.Chứng minh S chia hết cho 3;7;15

nhanh vs đúng mình ******* cho

Answer 1

S=1+2+2^2+2^3+...+2^59

S=(1+2)+(2^2+2^3)+...+(2^58+2^59)

S=3+2^2(1+2)+...+2^58.(1+2)

S=3+2^2.3+...+2^58.3

S= 3.( 1+2^2+...+2^58) chia hết cho 3

S=1+2+2^2+2^3+...+2^59

S=(1+2+2^2)+(2^3+2^4+2^5)+...+(2^57+2^58+2^59)

S=7.2^3(1+2+2^2)+....+2^57(1+2+2^2)

S=7+2^3.7+...+2^57.7

S=7.(1+2^3+...+2^57) chia hết cho 7

S= 1+2+2^2+2^3+...+2^59

S=(1+2+2^2+2^3)+(2^4+2^5+2^6+2^7)+...+(2^56+2^57+2^58+2^59)

S=15+2^4(1+2+2^2+2^3)+...+2^56(1+2+2^2+2^3)

S=15+2^4.15+...+2^56.15

S=15(1+2^4+...+2^56) chia hết cho 15

chắc chắn đúng tick cho mình nhé!