Mastering Series Identification: Tips for Recognizing Types of Series

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I just started studying series and I was curious if there is any way to recognize the types of series i.e.(harmonic, geometric, telescoping etc.) without writing out the first five or so parts of the series. What strategies do some of you use when identifying the types of series?
 
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Practise lots of different questions and then it will become a lot easier and intuitive.
 

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 . 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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