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Please show me the way to solve this problem. I "believe" that differentiating it and/or integrating this problem would be a big mess. So the only thing I could think of is the comparison test. But how do we split this up so that it is comparable?
Are you allowed to use the ratio test? In case you are not familiar with the ratio test, here is a link an article on Wolfram about it: Ratio Test -- from Wolfram MathWorld
Basically, if $\displaystyle a_n$ is the nth term of the series and $\displaystyle \displaystyle \lim_{n \to \infty} \dfrac{a_{n+1}}{a_n} < 1$, then the series converges.
just compare it to the geometric with r=.25, since (n-1)/n is less than 1.
