Question

For the the following series determine whether it converges or

diverges — if it converges, find the limit. It is either geometric
or telescoping.

Answer 1

A geometric series converges if the absolute value of the common ratio is less than 1 and diverges otherwise. The limit of a geometric series can be found using the formula: Limit = (first term)/(1 - common ratio).

Step-by-step explanation:

A series is said to converge if the sum of its terms approaches a finite value as the number of terms increases. On the other hand, a series is said to diverge if the sum of its terms grows without bound as the number of terms increases. To determine whether a series converges or diverges, we need to examine its pattern.

In the case of a geometric series, each term is found by multiplying the previous term by a fixed, non-zero number called the common ratio. The series converges if the absolute value of the common ratio is less than 1 and diverges otherwise. The limit of a geometric series can be found using the formula:

Limit = (first term)/(1 - common ratio).