Determine whether or not the following series converges.
A) Converges
B) Diverges
C) Cannot be determined

Question

Determine whether or not the following series converges. 
A) Converges 
B) Diverges 
C) Cannot be determined

Quizplus · Accepted Answer

We cannot determine the exact value of the series from the given information, but we can say that it converges because it is a geometric series with a common ratio |r|<1. A geometric series with |r|<1 converges to a finite value given by the formula S=a/(1-r), where 'a' is the first term and 'r' is the common ratio. Since we know that |r|<1, the denominator 1-r will always be positive, so as we add more and more terms to the sequence, the sum will approach the finite value of a/(1-r). Therefore, the series converges.

Determine Whether or Not the Following Series Converges