I’ve been playing around with the infinite series:(adsbygoogle = window.adsbygoogle || []).push({});

[tex] \sum_{k=1}^\infty \frac{k}{(k+1)!} [/tex]

I haven’t really gotten anywhere with it however I punched it into my calculator and it determined the sum to be 1. And the sum of n terms of the series equals

[tex]1-\frac{1}{(n+1)(n!)} [/tex]

Why is this so? Any help is much appreciated.

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# Series and factorial

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