Wednesday, March 29, 2017

Convergence and sum of an infinite series: $sum_{i=1}^{infty}frac{6}{24 i-4 i^2-35}$

Determine whether the following series is convergent or divergent. If convergent, find the sum. $$\sum_{i=1}^{\infty}\frac{6}{24 i-4 i^2-35}$$


Since the limit of the series is zero, I know that it is not divergent (divergence test).


How do i prove that the series is convergent, and futhermore, find the sum?


I rewrote the series (using partial fraction decomposition) as:



$$\sum_{i=1}^{\infty}\frac{6}{24 i-4 i^2-35}=\sum_{i=1}^{\infty}\frac1{1/4i-10(-(1/4 i-7))}$$


But I don't know what to do from here.

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