Tuesday, 25 April 2017

real analysis - How to calculate $sumfrac{1}{(4k-1)(4k+4)}$?

I'm trying to calculate $\sum_{k=1}^\infty\frac{1}{(4k-1)(4k+4)}$ using telescopic sums. I've already proved this equality: $\sum\frac{1}{(4k-1)(4k+4)}=\frac{1}{5}\big(\sum\frac{1}{4k-1}-\frac{1}{4k+4}\big)$. The problem is I can't cancel the terms of this sum.



I need help



Thanks

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