The sum
\sum_{k=0}^{\infty} \frac{2^k}{5^{2^k}+1}
can be written in the form \frac{P}{q} where p and q are relatively prime positive integers. Find p+q.
The sum
\sum_{k=0}^{\infty} \frac{2^k}{5^{2^k}+1}
can be written in the form \frac{P}{q} where p and q are relatively prime positive integers. Find p+q.