Question

[Lê Quang Trung]

Bài 11:Chứng minh tổng sau chia hết cho 7

A=2¹+2²+2³+2⁴+......+2⁵⁹+2⁶⁰

Answer 1

[Nguyễn Thị Huyền Trang]

\(A=2^1+2^2+2^3+...+2^{60}\)

\(=\left(2^1+2^2+2^3\right)+...+\left(2^{58}+2^{59}+2^{60}\right)\)

\(=\left(2.1+2.2+2.2^2\right)+...+\left(2^{58}.1+2^{58}.2+2^{58}.2^2\right)\)

\(=2.\left(1+2+4\right)+...+2^{58}.\left(1+2+4\right)\)

\(=2.7+...+2^{58}.7\)

\(=\left(2+2^{58}\right).7⋮7\)hay \(A⋮7\)

Answer 2

[Nicky Grimmie]

A=(2+2^2)+(2^3+2^4)+...+(2^59+2^60)

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

A=2.7+...+2^58.7

A=7(2+2^4+....+2^58) chia hết cho 7

vậy...