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`sum_(n=1)^oo arctan(n)/(n^2+1)` Confirm that the Integral Test can be applied to the series. Then use the Integral Test to determine the convergence or divergence of the series.

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`sum_(n=1)^ooarctan(n)/(n^2+1)`

Integral test is applicable if f is positive, continuous and decreasing function on infinite interval `[k,oo)` where `k>=1` and `a_n=f(x)` . Then the series `sum_(n=1)^ooa_n`  converges or diverges if and only if the improper integral `int_1^oof(x)dx` converges or diverges.

For the given series `a_n=arctan(n)/(n^2+1)`

Consider `f(x)=arctan(x)/(x^2+1)`

Refer the attached graph of the function. From the graph, we observe that the...

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