How do I find the sum of the following infinite series:
$$\frac{2}{5\cdot10}+\frac{2\cdot6}{5\cdot10\cdot15}+\frac{2\cdot6\cdot10}{5\cdot10\cdot15\cdot20 }+\cdots$$
I think the sum can be converted to definite integral and calculated but I don't know how to proceed from there.
Sunday 20 July 2014
Sum of the series $frac{2}{5cdot10}+frac{2cdot6}{5cdot10cdot15}+frac{2cdot6cdot10}{5cdot10cdot15cdot20 }+cdots$
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