Question

In 2-3 sentences describe why the only way an infinite geometric series has a sum is if |r| < 1.

Answer 1

Because if the common ratio less than 1, then each term is smaller than the previous term. eventually, it will be so small that it basically equals 0 and the next terms are nigligible

it's like this. say you are on one side of a playground
you walk half the distance across,
you then walk half of the disatnce you just walked
you then walk half of the disatnce you just walked
etc
you will never reach the other side because each distance you take is smaller thatn the previous, eventaull the distance will be so small you won't be moving much