Can the Summation Expression be Simplified?

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I am wondering whether the following expression can be simplified

sum of( (p^n) / (n!) ) from n=1 to n=n.
 
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It look pretty simple to me already. If you mean write it without the summation, I don't think so.
 


What do you mean by "n= n"? Did you mean
\sum_{n=1}^{N} \frac{p^n}{n!}?
I don't see any simple way to write that. However, it is well known that
\sum_{n=1}^\infty \frac{p^n}{n!}= e^p- 1
 
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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