How can a series of infinite numbers have a infinite answer?

Answer 1

Because infinite means never ending - therefore there can never be a final answer, but sometimes an infinite series will converge to a finite answer. An example of one that results in an infinite answer should be fairly easy. Consider 1+2+3+4+5+6+.... Each number is bigger than the previous. But what about when each term is smaller than the previous. Look at this one: 1/2 + 1/4 + 1/8 + 1/16 + 1/32 + .... Each term is 1/2 the previous term. As the terms are added, the sum of the series would look like this: 1/2, 3/4, 7/8, 15/16, 31/32,... Notice that each sum is half way between the previous sum and 1, but will never get to 1. We say this series converges to 1.

Not every series, where the terms decrease, will converge to a finite number though.