Harmonic Overdose

Algebra Level 5

If \(\displaystyle M=\sum_{n=1}^{1728}H_{n}H_{1729-n}\) and \(\displaystyle E=2\sum_{n=1}^{1728}H_{n}\left(\frac{1729-n}{n+1}\right)\), find \(\dfrac{1729M}{E}+\dfrac{1729E}{M}\).

\(\)

Notation: \(H_n\) is the \(n\)th harmonic number.

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