# An Unlucky Number?

**Algebra**Level 4

\[ \large \displaystyle \sum_{n=0}^\infty \frac {2^n}{13^{2^n} + 1} \]

The closed form of the above summation is equals to \(\frac p q \) for coprime positive integers \(p,q\). What is the value of \(p+ q\)?

\[ \large \displaystyle \sum_{n=0}^\infty \frac {2^n}{13^{2^n} + 1} \]

The closed form of the above summation is equals to \(\frac p q \) for coprime positive integers \(p,q\). What is the value of \(p+ q\)?

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