Combination of harmonic and geometric series – math.stackexchange.com

Combination of harmonic and geometric series – math.stackexchange.com

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I need to know $$\sum_{n=1}^{\infty} \frac{1}{2^n}\left(\frac11+\frac12+\frac 13+...+\frac1 n\right)$$has a close form solution ? It is easy to prove this series converge ,because ...

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