Đáp án:

 

Giải thích các bước giải:

Bài `5:`

`b=2^1+2^2+2^3+...+2^201`

`b=(2^1+2^2+2^3)+...+(2^199+2^200+2^201)`

`b=2(1+2+2^2)+...+2^199(1+2+2^2)`

`b=2*7+...+2^199*7`

`b=7(2+...+2^199)vdots7(đpcm)`

Vậy `...`

`---`

Bài `6:`

`c=5+5^4+5^7+5^10+....+5^2020`

`c=(5+5^4)+(5^7+5^10)+....+(5^2017+5^2020)`

`c=5(1+5^3)+5^7(1+5^3)+...+5^2017(1+5^3)`

`c=5*126+5^7*126+...+5^2017*126`

`c=126(5+5^7+...+5^2017)vdots9(đpcm)`

Vậy `...`

`---`

Bài `7:`

`a=3^0+3^1+3^2+...+3^30`

`3a=3+3^2+3^3+...+3^31`

`3a-a=3^31-3`

`a=(3^31-3)/2`

Vậy `...`