Practice (22)

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Compute: $\frac{1}{1\times 2\times 3} + \frac{1}{2\times 3\times 4} + \cdots + \frac{1}{2016\times 2017\times 2018}$

Compute $\frac{1}{1\times 2} + \frac{1}{2\times 3} + \cdots + \frac{1}{2017\times 2018}$

Let $n$ and $k$ be two positive integers. Show that $$\frac{1}{\binom{n}{k}}=\frac{k}{k-1}\left(\frac{1}{\binom{n-1}{k-1}}-\frac{1}{\binom{n}{k-1}}\right)$$