## sevenshaded 2 years ago Determine whether the series is convergent or divergent. If it is convergent, find its sum. Problem inside.

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

Actually, that should be k = 2 under the summation.

Basically, I know that the answer converges, but I don't know why. I would think that if the numerator was infinity squared and the denominator was infinity squared minus one, that the numerator was approaching infinity at a faster rate, thus making it diverge because it could just get bigger and bigger. But I guess that's incorrect reasoning.