Basic Series: Sum of 1/3 from i=1 to n

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Homework Statement


what is \sum i1/3 from i=1 to n


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The Attempt at a Solution


is there an expansion for this?
 
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As long as n is finite, the series will converge, but there is no closed form for this summation as terms get successively larger.

(unless the 'i' inside your sum is actually supposed to be \sqrt{-1} rather than an iterator)
 

Thread 'Finding the nth roots of a complex number'

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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