\(1+7+7^2+...+7^{99}=\left(1+7\right)+7^2\left(1+7\right)+7^4\left(1+7\right)+...+7^{98}\left(1+7\right)\)
\(=\left(1+7\right)\left(1+7^2+...+7^{98}\right)=8\left(1+7^2+...+7^{98}\right)⋮8\left(đpcm\right)\)
Ta có : \(1+7+7^2+7^3+...+7^{99}\)
\(=\left(1+7\right)+\left(7^2+7^3\right)+...+\left(7^{98}+7^{99}\right)\)
\(=\left(1+7\right)+7^2.\left(1+7\right)+...+7^{98}.\left(1+7\right)\)
\(=8+7^2.8+....+7^{98}.8\)
\(=8.\left(1+7^2+...+7^{98}\right)⋮8\)
\(\Rightarrow1+7+7^2+7^3+...+7^{99}⋮8\left(đpcm\right)\)
Ta có: 1 + 7 + 72 + 73 + ... + 799 (gồm 100 số hạng)
= (1 + 7) + (72 + 73) + ... + (798 + 799) (gồm 50 cặp số hạng)
= 8 + 72(1 + 7) + ... + 798(1 + 7)
= 8 + 72.8 + ... + 798.8
= 8.(1 + 72 + .... + 798) \(⋮\)8
Vậy ...
\(1+7+7^2+7^3+...+7^{99}\)
\(=\left(1+7\right)+\left(7^2+7^3\right)+...+\left(7^{98}+7^{99}\right)\)
\(=\left(1+7\right)+7^2\left(1+7\right)+...+7^{98}\left(1+7\right)\)
\(=8+7^2\cdot8+...+7^{98}\cdot8\)
\(=8\left(1+7^2+...+7^{98}\right)⋮8\) (đpcm)
=))
\(1+7+7^2+...+7^{99}=\left(1+7\right)+7^2\left(1+7\right)+7^4\left(1+7\right)+...+7^{98}\left(1+7\right)\)
\(=\left(1+7\right)\left(1+7^2+...+7^{98}\right)=8\left(1+7^2+...+7^{98}\right)⋮8\left(đpcm\right)\)
thanks các bạn nhiều nha!!!!!!!!!!!!!!!!!!!!!!!!!!
