Mathegoras

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Ratio of weighted harmonic sums

High school · ●●●○○ 50 pts

Determine the value of 20161+20152+20143+⋯+1201612+13+14+⋯+12017\frac{\frac{2016}{1} + \frac{2015}{2} + \frac{2014}{3} + \dots + \frac{1}{2016}}{\frac{1}{2} + \frac{1}{3} + \frac{1}{4} + \dots + \frac{1}{2017}}.

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harmonic numberstelescoping sums