Powers of 2 and harmonic numbers

Calculus Level 3

Let Hn=1+12+13++1n H_n = 1+\frac12 + \frac13 + \cdots + \frac1{n} be the nthn^\text{th} harmonic number.

The sum n=1Hn2n=ln(a)\displaystyle \sum_{n=1}^\infty \frac{H_n}{2^n} = \ln (a) for some positive integer a. a.

What is a? a?

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