# Harmonic numbers and sums

Calculus Level 5

$\displaystyle \sum _{ n=1 }^{ \infty }{ { \left(\frac { { H }_{ n } }{ n } \right) }^{ 2 } }$

If the above summation can be stated in the form $$\dfrac { A{ \pi }^{ B } }{ C }$$ for positive integers $$A,B,C$$ with $$\text{gcd}(A,C) = 1$$.

What is the value of $$A+B+C$$?

Details and Assumptions

$$H_n$$ is the $$n^\text{th}$$ Harmonic number, $$\displaystyle {H}_{n} = \sum _{ r=1 }^{ n }{ \frac { 1 }{ r } }$$

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