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How to evaluate these two euler sums?

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Post Thu May 05, 2016 4:45 pm

Posts: 4
Location: Linyi,China

How to evaluate
$$\sum_{n=1}^{\infty}\frac{H_n}{n^52^n}~~,~~\sum_{n=1}^{\infty}\frac{H_n}{n^62^n}$$
In [this post][1] M gives a closed form for the first series,but it contains a zeta function,can it be simplified any more? And is there a closed form for the second series.

[1]: http://math.stackexchange.com/questions ... 2xxdx?lq=1
Integrals and Series Zealot.

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