real analysis - How to calculate the value of
$sumlimits_{k=0}^{infty}frac{1}{(3k+1)cdot(3k+2)cdot(3k+3)}$?
How do I calculate the value of the series $$\sum_{k=0}^{\infty}\frac{1}{(3k+1)\cdot(3k+2)\cdot(3k+3)}= \frac{1}{1\cdot2\cdot3}+\frac{1}{4\cdot5\cdot6}+\frac{1}{7\cdot8\cdot9}+\cdots?$$
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