This is a finite geometric series:
Originally Posted by 0123
Now you could look up the formula for the sum of a finite geometric series or
derive it form the observation that:
since if you multiply out the brackets on the left all but the first and last
terms in the result cancel out.
So we have:
for any and , and so in particular for our
series, where , and .
>.. bute force sum of series:
>.. CaptainBlack's formula for sum of series:
>S6 = (1-1/1.3^(7/12)) / (1-1/1.3^(1/12))-1