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Determine if the following series converges or diverges:
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.
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.