infinity over Sigma n=1 n^2/n^3 + 1 Use the integral test to see if the infinite series converges.
infinity over Sigma n=2 n^2+1/n^3.5-2 Use either the Comparison Test or the Limit Comparison Test to see if the infinite series converges.
infinity over Sigma n=1 n^2/n^3 + 1 Use the integral test to see if the infinite series converges.
infinity over Sigma n=2 n^2+1/n^3.5-2 Use either the Comparison Test or the Limit Comparison Test to see if the infinite series converges.
Put then is a positive, continuous and decreasing function for hence, the integral test applies and the series will converge or diverge if does.
Since then the integral diverges, so does the series. (Actually, one can bound immediately the general term of the series rather than applying the integral test.)
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As for your second question, compare the series with which is a convergent series with
So, put and and observe that so your series converges.