Sandeep's Harmonic Sums

Algebra Level 4

For each positive integer \(n\), let \[H_n = \frac{1}{1} + \frac{1}{2} + \cdots + \frac{1}{n}.\] If \[ \sum_{n=4}^{\infty} \frac{1}{nH_nH_{n-1}} = \frac{a}{b} \] for relatively prime positive integers \(a\) and \(b\), find \(a+b\).

This problem is shared by Sandeep S.

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