Question

A=3+3²+3³+3⁴+.....+3^2n-1+3²ⁿ

Tổng A có Chia hết cho 4 không?Vì Sao?

Thanks ........................................................................................................very much .............................................................hjhj

Answer 1

Ta có:A=\(3+3^2+3^3+3^4+...+3^{2n-1}+3^{2n}\)(có 2n số hạng)

A=\(\left(3+3^2\right)+\left(3^3+3^4\right)+...+\left(3^{2n-1}+3^{2n}\right)\)(có n nhóm)

A=\(3\left(1+3\right)+3^3\left(1+3\right)+...+3^{2n-1}\left(1+3\right)\)

A=\(3\cdot4+3^3\cdot4+...+3^{2n-1}\cdot4\)

A=\(4\left(3+3^3+...+3^{2n-1}\right)⋮4\)

Vậy A\(⋮4\)