Question

Find the sum of `2 + 2^2 + 2^3 + 2^4 + 2^5....... 2^n`?

Answer 1

The answer is `=2(2^n-1)`

Explanation:

This is a geometric series, the common ratio is `r=2`

`S=2+2^2+2^3+.........2^n`

`2S=2^2+2^3+.................+2^(n+1)`

`2S-S=2^(n+1)-2`

`S=2(2^n-1)`