Question

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

Answer 1

The formula for the sum of geometric series = a (1 - r^n) / 1 - r
when it will be an infinite geometric series. the term r^n will equal to zero because and number < 1 that is raise to the power infinity the answer is zero that is why in a infinite geometric series, sum = a / 1 - r.
if the r < 1 then there will be no numerical answer because the sum will be infinity. that is why r < 1 to have a sum