Finding the Interval for Power Series Summation of x^(n)/[2^(n)*n^(4)]

frasifrasi
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For summation from 1 to infinity of x^(n)/[2^(n)*n^(4)]
- I get the radius is 2 by ration test, but how do I get the interval, just by pluggin in?
 
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anyone? : )
 
well it's just -1<x<1

so your R is 2, but before you had x/2

-1<x/2<1

-2<x<2 (equal to)
 
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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