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Hey guys I have this homework problem that I am having difficulty explaining. The question is why the integral comparison test cannot be used. The Series is:

The sum of the indefinite series from n=1 to infinity is equal to cos^2(n)/(1+n^2).

I see that the series is positive and is continuously decreasing, but I can't seem to find the integral of the series and explain why you can't use the integral comparison test.

Thanks for all the help!

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The sequence is not decreasing because values of $\cos^2n$ fluctuate between $0$ and $1$. So, the best you can say about is that $0<\cos^2n/(1+n^2)<1$.

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