Sandeep's Harmonic Sums

Algebra Level 3

For each positive integer nn, let Hn=11+12++1n.H_n = \frac{1}{1} + \frac{1}{2} + \cdots + \frac{1}{n}. If n=41nHnHn1=ab \sum_{n=4}^{\infty} \frac{1}{nH_nH_{n-1}} = \frac{a}{b} for relatively prime positive integers aa and bb, find a+ba+b.

This problem is shared by Sandeep S.

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