Power Series Problem: Am I Correct?

temaire
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Homework Statement


Well, I'm not getting any problems from the question, but there is a part of the solution that I don't agree with.

Here's the problem statement:
[PLAIN]http://img810.imageshack.us/img810/5387/powerseriesproblem.png

Here's part of the solution:
[PLAIN]http://img38.imageshack.us/img38/2104/powerseries.png


The Attempt at a Solution


As you can see, in the solution I circled +1 in red. I don't think it should be there. Instead, I think outside the right square bracket there should be + a_n

Am I correct?
 
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I agree with you. Looks like there's a mistake in the solutions.
 
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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