# 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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