Understanding the \Pi Notation for Calculus Homework | Help and Explanation

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Homework Statement


\Pi_{n=1}^{5} n


Homework Equations


My teacher assumed I learned this in calc 2 but I was never taught this. Can someone tell me what this thing is called?
 
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It means a "product", like a capital sigma means a "sum", and you interpret it the same way. So this reads, "the product of n, from n=1 to n=5", in other words 1*2*3*4*5, which in this case equals 5!.
 
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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