How to simplify this summation: $\frac{2\sum_{k=0}^n2^n}{n+1}=2^{n+1}$?

Question

So I saw an earlier post where they had this equation here.

$\frac{2\sum_{k=0}^n2^n}{n+1}=2^{n+1}$?

However, I do not know how they did this? Am I missing something?

Answer 1

If the expression is correct $$\frac{2\sum_{k=0}^n2^n}{n+1}=\frac{2\times 2^n}{n+1}\sum_{k=0}^n1=\frac{2^{n+1}}{n+1}(n+1)=2^{n+1}$$

Answer 2

Hint: $\sum_{k=0}^n 2^n=2^n\cdot (n+1)$ Note, that $2^n$ have no index k.