Mastering Series in Calculus: Tips and Encouragement for Success

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I just finished improper integrals and am about to learn series in my calc class. Does anyone have any advice/words of encouragement?
 
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Realize there are two fundamental questions with series. Does it diverge or converge and if it converges what is it's sum. The former you will learn a lot of the test, that latter you will rarely find the answer.
 
You'll probably start with simple geometric series, which are easy to sum and determine convergence, and (if it's AP Calc) go up to Taylor Polynomials, which are used to approximate transcendental functions (among other things). Make sure that you learn all of the tests for convergence, and try to recognize patterns in the series. Often times you'll be given series that resemble one of your formulas, and you have to manipulate the series so that it resembles that formula, at which point you can apply a test.
 

Thread 'Finding the nth roots of a complex number'

There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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