Find the sum of the series Σ((3n+2)/n).... (confirmation)

Michael_0039
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Homework Statement
Find the sum of the series Σ((3n+2)/n!)
Relevant Equations
nil
Hi,
this is my try:
XMyAop0.jpg
Thanks.
 
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Looks good. You could have added a first step: ##\displaystyle \sum_{i=0}^\infty \frac{3n}{n!} = \sum_{i=1}^\infty \frac{3n}{n!}## as 3*0=0.

(formula written with LaTeX)
 
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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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