# How do you determine whether the series is convergent or divergent given #sum (sin^2(n))/(n*sqrt(n))# for n=1 to #n=oo#?

Converges by the Comparison Test.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

- How do you apply the ratio test to determine if #sum_(n=1)^oo (e^n(n!))/n^n# is convergent or divergent?
- How do you determine if the improper integral converges or diverges #int sec^2 x dx# from negative 0 to pi?
- How do you use the integral test to determine the convergence or divergence of #1+1/sqrt2+1/sqrt3+1/sqrt4+...#?
- How do you test the improper integral #int (x(1+x^2)^-2)dx# from #[0,oo)# and evaluate if possible?
- How do you use the Integral test on the infinite series #sum_(n=1)^oo1/n^5# ?

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