Question-22062

Question Number 22062 by x² – y²@gmail.com last updated on 10/Oct/17

Commented by FilupS last updated on 10/Oct/17

= \underset{n = 1}{\sum^{97}} \frac{1}{(n + 1)! \cdot (n + 3)!}

= \underset{n = 1}{\sum^{97}} \frac{1}{(n + 1)!^{2} \cdot (n + 2) (n + 3)}

= ? ? ?

Answered by $@ty@m last updated on 11/Oct/17

= (\frac{1}{3!} - \frac{1}{4!}) + (\frac{1}{4!} - \frac{1}{5!}) + (\frac{1}{5!} - \frac{1}{6!}) + \dots + (\frac{1}{99!} - \frac{1}{100!})

= \frac{1}{3!} - \frac{1}{100!}

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