This is a similar question that I have to the other one that I posted.(adsbygoogle = window.adsbygoogle || []).push({});

Determine if the following series converges or diverges.

sum[k=1,inf] 3/(k(k+3))

I applied the limit comparison test with 1/k^2

also k(k+3))=k^2+3k

lim k->inf [ 3/(k^2+3k) ]/[ 1/k^2 ] = lim k->inf (3k^2/(k^2+3k) =H 3

because sum[k=1,inf] 1/k^2 is a convergent p-series than sum[k=1,inf] 3/(k(k+3)) must also converge by the limit comparison test.

I plugged this into wolfram alpha

sum[n=1,inf] of 3/(k(k+3))

and it said that the sum does not converge by the limit comparison test. Am I doing something wrong?

Thanks for any help.

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# Calculus 2 - Infinite Series

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