Ta có:
A=1+21+22+...+2100+2101A=1+21+22+...+2100+2101
= (1+2+22)+(23+24+25)+...+(299+2100+2101)(1+2+22)+(23+24+25)+...+(299+2100+2101)
= (1+2+22)+22.(1+2+22)+...+299.(1+2+22)(1+2+22)+22.(1+2+22)+...+299.(1+2+22)
= (1+2+22).(1+22+26+...+299)(1+2+22).(1+22+26+...+299)
= 7.(1+22+26+...+299)⋮77.(1+22+26+...+299)⋮7
(Vì 7⋮7)
\(A=1+2^1+2^2+...+2^{100}+2^{101}\)
\(\Rightarrow A=\left(1+2^1+2^2\right)+\left(2^3+2^4+2^5\right)+...+\left(2^{99}+2^{100}+2^{101}\right)\)
\(\Rightarrow A=\left(1+2^1+2^2\right)+2^3\left(1+2^1+2^2\right)+...+2^{99}\left(1+2^1+2^2\right)\)
\(\Rightarrow A=\left(1+2^1+2^2\right)\left(1+2^3+...+2^{99}\right)\)
\(\Rightarrow A=7\left(1+2^3+...+2^{99}\right)⋮7\)
