We have to check the given series
is convergent or divergent using the limit comparision test.
According to limit comparision test if two series and with for all n.
Then if with 0 then either both series converges or both series divergent.
Take common highest power n from denominator and numerator we get
Let another series
is convergent p-series since p=3
which is finite and positive.
Therefore we can conclude by limit comparison test series will be convergent.
So given series is convergent.