My book has writen this. Series is attached

How he has converged the series

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- Jun 11th 2010, 09:01 AMmoonnightingaleQuestion about Series convergance
My book has writen this. Series is attached

How he has converged the series - Jun 11th 2010, 09:03 AMHallsofIvy
That's

**almost**a geometric series. There is a general formula that

$\displaystyle \sum_{n=0}^\infty ar^n= \frac{a}{1- r}$.

Now, the derivative, term by term, is $\displaystyle \sum_{n=0}^\infty a_n r^{n-1}$ and that must be equal to the derivative, with respect to r, of $\displaystyle \frac{a}{1- r}$. - Jun 11th 2010, 09:15 AMmoonnightingale
Why book has used (Square) in denominator???