Question

Find the sum of the following infinite geometric series, if it exists. 2 + 6 + 18 + 54 +… Does not exist 23,567 25,982 29,034

Answer 1

Option A: The sum for the infinite geometric series does not exist

Explanation:

The given series is $2+6+18+54+.......$

We need to determine the sum for the infinite geometric series.

Common ratio:

The common difference for the given infinite series is given by

$r=\frac{6}{2}=3$

Thus, the common difference is $r=3$

Sum of the infinite series:

The sum of the infinite series can be determined using the formula,

$S_{\infty}=\frac{a}{1-r}$   where $0<r<1$

Since, the value of r is 3 and the value of r does not lie in the limit $0<r<1$

Hence, the sum for the given infinite geometric series does not exist.

Therefore, Option A is the correct answer.