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opus

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## Homework Statement

Use the integral test to compare the series to an appropriate improper integral, then use a comparison test to show the integral converges or diverges and conclude whether the initial series converges or diverges.

##\sum_{n=3}^\infty \frac{n^2+3}{n^{5/2}+n^2+n+1}##

## Homework Equations

## The Attempt at a Solution

I'm really just at a loss on what to do here. I went to the tutor lab on campus and three tutors (one of which was the class TA) couldn't answer this question.

So to start somewhere, I can compare this series to an integral via the integral test. However, to use this test, I would need to evaluate the integral and to my understanding the integrand of the integral would be of the form ##f(n)=a_n## for all integer values n greater than or equal to 3. My first problem is that there is no way I can evaluate ##\int_3^\infty \frac{x^3+3}{x^{5/2}+x^2+x+1}dx##. So there must be something else that I can do, but I'm not sure what. Any ideas?