Question

Identify whether the series is a convergent or divergent geometric series and find the sum, if possible.

This is a convergent geometric series. The sum cannot be found.
This is a divergent geometric series. The sum cannot be found.
This is a convergent geometric series. The sum is –4.
This is a divergent geometric series. The sum is –4.

Answer 1

this is a divergent geometric series. the sum cannot be found

Answer 2

Explanation:

There is a series given which can be written in expanded form as

16+16(5)+16(5^2)+....

16 is a common factor to all

Hence

=16(1+5+5^2+5^3+...+5^n+...)

We find that this is a geometric series with I term =1 and common ratio = 5

Since 5, the common ratio is >1, the infinite series sum will diverge

Hence the series is a geometric series with infinite sum diverging.

Correct answer is:

This is a divergent geometric series. The sum cannot be found.