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GreenPrint
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This is a similar question that I have to the other one that I posted.
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.
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.