Question

Find the sum of the following infinite geometric series, if it exists.

Answer 1

Answer:  Does not exist

Step-by-step explanation:

The given geometric series : $60 + 84 + 117.6 + 164.64 +…$

Here the first term : $a=60$

The second term : $ar=84$

Now, the common ratio in this series will be :_

$r=\dfrac{ar}{a}=\dfrac{84}{60}=1.4>1$

We know that if the common ratio in infinite geometric series does not lies between (-1,1) , then the series is diverging. And the sum of the infinite geometric series will not exists.

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

Answer 2

$q=\dfrac{84}{60}=1.4 > 1\ \text{ therefore you answer: Does not exist}$