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Ʃ[k=1,inf] ( k^2-1 )/( k^3+4 )

I don't see how to solve this problem

the divergence test is inconclusive

the ratio test is inconclusive

the root test is inconclusive

the integral test... not sure how to integrate this...

the comparison test... I thought about comparing it to k^2/k^3=1/k but because 1/k > ( k^2-1 )/( k^3+4 ) and Ʃ 1/k is the divergent harmonic series so we cannot conclude anything

the limit comparison test... Not sure what to use for the other series but 1/k and

lim k->inf (k(k^2-1))/(k^3+4) = 0 but because 1/k is divergent harmonic series I don't know how to apply the comparison test in this case... we could conclude that the original series converges if Ʃ1/k converged to but sense it doesn't I don't think I can conclude anything from this... there's only 3 cases from the limit comparison test that which we can conclude something from, what do we do in a situation like this were it's not one of those cases???

this is not a p-series

this is not a geometric series

I'm lost as to what to do. Thanks for any help.