How do I evaluate the sum $\sum_{n=0}^{\infty}\frac{2^{n}}{2^{2^{n}}+1}$?

Question

The series clearly converges, but I have no idea how to approach it using basic methods. How do I solve it?

score 1 · Accepted Answer · answered Nov 30 '23 at 15:50

1

It is know that $\sum_{n=0}^\infty\frac{2^nx^{2^n-1}}{1+x^{2^n}}=\frac{1}{1-x}$ for all $|x|<1$. Now just take $x=1/2$.

answered Nov 30 '23 at 15:50

Michael Rincon

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