Find an+1 in Alternating Series: Is Plugging in "n+1" Right?

Ki-nana18
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I'm confused as to how to find an+1. I can figure out how to find the limit of an, which is the first component of the alternating series test. How do you find an+1? I'm thinking you just plug in "n+1" for "n" is that right?
 
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If you're working with a summation, you have a formula for an. If you want an+1, substitute n+1 instead of n in the formula for an.
 
Thank you! According to the back of the book I got the right answer. YES!
 
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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