Provide an appropriate response. -The sum of an infinite geometric series exists if: A) $| r | \leq 1$ B) $| \mathrm { r } | 1$

Question

Provide an appropriate response.
-The sum of an infinite geometric series exists if:
A) $| r | \leq 1$

B) $| \mathrm { r } | < 1$

C) $| r | \geq 1$

D) $| \mathrm { r } | > 1$

Quizplus · Accepted Answer

The sum of an infinite geometric series exists and is finite if and only if the absolute value of the common ratio $r$ is less than 1, i.e., $| r | < 1$. This condition ensures that the terms of the series approach zero as the number of terms increases.

Provide an Appropriate Response ∣r∣≤1| r | \leq 1∣r∣≤1 B) ∣r∣<1| \mathrm { r } | < 1∣r∣<1

Provide an Appropriate Response $| r | \leq 1$ B) $| \mathrm { r } | < 1$