Bino Harmonic Series 1

Calculus Level 5

\[ \text{S} = \sum_{n=1}^{\infty} \left [\dbinom{2n}{n} \cdot \dfrac{H_{n}}{2^{2n}(n+1)}\right] \]

\(\text{S}\) can be written as \(\text{A}^{\text{B}} \ln \text{C}\), where \(\text{A}\), \(\text{B}\) and \(\text{C}\) are all positive integers greater than \(1\) and \(\text{C}\) is a prime number.

Evaluate \( \text{A}+\text{B}+\text{C}\)

Note : \(H_{n}\) is the \(\text{n}^{\text{th}}\) Harmonic Number.


See Also : Part 2

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