# A Harmonic Sum

Calculus Level 5

$\displaystyle \sum_{n=1}^\infty \frac { (H_n )^2}{2^n} = \frac {\pi ^a}{b} + \log ^2 (c)$

Let $$H_n$$ denote the $$n^{\text{th}}$$ harmonic number such that the above series is satisfied for positive integers $$a,b,c$$.

Find $$a+b+c$$.

Details and Assumptions

• $$H_n = 1 + \frac 1 2 + \frac 1 3 + \ldots \frac 1 n$$ for $$n = 1,2,3, \ldots$$

• $$\log$$ is a natural logarithm

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