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Determine whether the series is convergent or divergent. If it is convergent, find its sum. Problem inside.

Mathematics
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\[\sum_{2}^{\infty} \frac{ k^{2} }{ k^{2}-1}\]
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.

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Other answers:

Secondly, I'm trying to put it into Ar ^ n format to begin to find the sum. I tried using k^2 times (k^2 - 1) ^-1 but I'm not sure if that's correct either.

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