# A perfectly natural question ....

Calculus Level 5

It is the case that

$$\displaystyle\sum_{n=1}^{\infty} \dfrac{1}{2^{n} * (n - \frac{1}{2})} = \sqrt{a}*\ln(b + \sqrt{c})$$,

where $$a,b,c$$ are positive integers with $$a$$ and $$c$$ being square-free.

Find $$a^{b+c}$$.

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