# Limit of a Harmonic Sum

Calculus Level 5

$\large \lim_{n \to \infty} \left[ H_{n} - \dfrac{1}{2^n} \sum_{r=1}^{n} \dbinom{n}{r} H_{r} \right] = \ln m$

If the equation above holds true, find $$m^2$$.

Notation: $$H_n$$ denotes the $$n^\text{th}$$ harmonic number, $$H_n = 1 + \dfrac12 + \dfrac13 + \cdots + \dfrac1n$$.

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