Improve Your Summation Formula with Expert Tips and Tricks | B(t)=a * b^t

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I am trying to Sum the total from the following equation B(t)=a * b^t

So I have \sum a * b^t with t=1 to 321

Trying to solve for an equation and getting a(b^(t+1) - 1) / (b-1)

Answer is not correct...help
 
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The answer you are presenting is for t starting at 0 not 1. The correct result would be:
ab(b321 - 1)/(b - 1).
 
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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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