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I'm currently in a Calculus II and Analytic Geometry course at my college. The work I did below is incomplete and contains errors probably. The little bit of u-substitution I ignored because I forgot that was meant for integration (been doing math for like 10 hours today, and I'm tired) this happens all the time: Ahhh

I needed to take the derivative to show that f'(x) was positive for all x >= 1 because that is one of the hypotheses of the integral test, and I have to test against all of them. So it's a quotient rule, that leads into a product rule, yuck.

I know an answer can't fix my problem, but I'm looking for a place to start so that I can begin improving my ability to write math equations by hand.

Glorfindel
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michaelsnowden
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    Do you know about asymptotic comparisons? This series behaves asymptotically like $\frac1{n^2}$. To show that $f$ is monotonically decreasing you could, instead of showing that the derivative is negative, just as well test $f(x)>f(y)$ for $x<y$ using algebraic transformations. And the derivative of a constant like 1 is zero. -- As for writing things up, use more text, much more prosa. Announce what calculation you are going to carry out and why. – Lutz Lehmann Feb 24 '14 at 07:18
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    "I'm currently in a Calculus II and Analytic Geometry course at my college." Then go see your teacher. It is part of her job to answer questions exactly like yours, and she is the one in the best position to do so, or to point you towards other resources at your institution. – Gerry Myerson Feb 24 '14 at 09:45

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