Help finding the limit of this series

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February 15th 2010, 03:57 PM
paupsers

Help finding the limit of this series

$\sum_{k=2}^\infty ln\frac{k^2-1}{k^2}$

I'm trying to figure out how to find the limit of this series. Any advice?
February 15th 2010, 04:30 PM
General

Quote:

Originally Posted by paupsers

$\sum_{k=2}^\infty ln\frac{k^2-1}{k^2}$

I'm trying to figure out how to find the limit of this series. Any advice?

$\frac{k^2-1}{k^2}=\frac{k-1}{k} \,\ \frac{k+1}{k}$ .

Apply:

$ln(ab)=ln(a)+ln(b)$ . for $a,b>0$ .

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