An Alternating Binomial Sum

★ 8/10combinatorics Recursion algebra Binomial Theorem

Problem

Evaluate

S = \frac{1}{2017}\binom{2017}{0} - \frac{1}{2016}\binom{2016}{1} + \frac{1}{2015}\binom{2015}{2} - \cdots - \frac{1}{1010}\binom{1010}{1007} + \frac{1}{1009}\binom{1009}{1008}.

Answer

Solution

Difficulty	8/10
Topics	combinatorics, Recursion, algebra, Binomial Theorem

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