Convolution of Unit Step and Impulses

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Homework Statement



attachment.php?attachmentid=51811&stc=1&d=1349999165.jpg


Homework Equations





The Attempt at a Solution



See the 2 figures attached below.

Am I doing this correctly? Is the result I obtained correct? Is there a easier way I could've solved this problem?

Thanks again!
 

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Bump, still looking to get my work checked over.
 
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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