Geometric Series - Problem 12

The capital letter Sigma in Greek tells us to do a sum. The number on the bottom is where we should start our substitution for the variable, and the number on the top tells us where to stop. Since the number on top is infinity, we will need to make sure that our ratio, r, between successive terms is between zero and one to make an infinite sum even possible. (If the absolute value of the r ratio is greater than one, then we say the infinite sum diverges.) The ratio r is the base of the exponential part of the sigma formula. We put in the first substitution value to find the first term in the sequence, then use the formula of the first term divided by the difference of 1 - r.