Describe why the only way an infinite geometric series has a sum is if |r| < 1.

An infinite geometric series is the sum of an infinite geometric sequence. This series would have no last term. The general form of the infinite geometric series is a1 + a1 r + a1 r2 + a1 r3 + ... a1 + a1 r + a1 r2 + a1 r3 + ..., where a1 a1 is the first term and rr is the common ratio.