Thursday, 15 November 2018

Sum of series $frac {4}{10}+frac {4cdot7}{10cdot20}+ frac {4cdot7cdot10}{10cdot20cdot30}+cdots$

What is the sum of the series



$$\frac {4}{10}+\frac {4\cdot7}{10\cdot20}+ \frac {4\cdot7\cdot10}{10\cdot20\cdot30}+\cdots?$$



I know how to check if a series is convergent or not.Is there any technique to find out the sum of a series like this where each term increases by a pattern?

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