This series converges and since all the terms are positive it converges absolutely.
One way to prove convergence is that term by term the given sequence is less than 1/n6 which converges; therefore the given series converges by the comparison test.
Paul M.
tutor
For the comparison test all you need is a convergent series with bigger terms than the one you are considering (divergent smaller series if you want to prove divergence).
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04/08/20
Paul M.
tutor
I looked at it already & wasn’t sure. I will try to look at it again.
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04/08/20
Jenny P.
Thank you. Why did you pick 1/n^6 and not n/sqrt (n^5) which is 1/n^3/2?04/08/20