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!


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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