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Calculus I, II, II, and differential equations
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Apr 19, 2015

The chapter on series is notorious for making calculus students want to hurl their textbooks into a fire, curl up into a fetal position, and sob uncontrollably the night before the exam (I've been there myself).

Honestly, its not that series are so difficult as much as it requires you to remember a lot of rules, how to apply them, and most importantly, in what order to apply them. And most calculus courses just don't do all that great a job of explaining this - they just hurl a bunch of theorems at you, a few tests, and tell you to sort it all out yourself. To help with this, I've created a flowchart that explains how to approach solving a mathematical series. The important things to keep in mind are:

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Gotta love xkcd...

Calculus 2, Math141
Apr 19, 2015

Thanks xkcd. You're always there to pick up the slack.

XKCD - Integration by parts

Mar 27, 2015

If you're reading this post, you've probably arrived at the point in your calculus course where they try to teach you how to do integration by partial fraction expansion. And if you're anything like I was when I first learned calculus, you're probably scratching your head and going whadafuhhhh? What is the point of all this?

Here's what you need to know. Partial fraction expansion is not an integration technique. It's an algebraic technique. That being said, it's useful for making certain algebraic expressions (i.e. rational expressions) easier to integrate by breaking them into smaller, simpler chunks. Sound familiar? Its that same mode of thinking that all your other calculus classes are pushing at - taking a difficult problem, decomposing it into several easier problems, and then putting the pieces back together.

Got it? Let's get down to business. Here's our problem:

Rewrite the following expression as the sum of three partial fraction terms: \[\frac{1}{(x-1)(x^2+x+1)}\]

Just to quickly review the step...

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