Question

Identify whether the series summation of 12 open parentheses 3 over 5 close parentheses to the i minus 1 power from 1 to infinity is a convergent or divergent geometric series and find the sum, if possible. (2 points) This is a convergent geometric series. The sum cannot be found. This is a convergent geometric series. The sum is 30. This is a divergent geometric series. The sum cannot be found. This is a divergent geometric series. The sum is 30.

Answer 1

Answer:

  This is a convergent geometric series. The sum is 30.

Step-by-step explanation:

In your series, the ratio of terms is 3/5, a value whose magnitude is less than 1. That means the series is convergent. The sum is given by the formula ...

  S = a1/(1 -r)

where a1 is the first term (12) and r is the common ratio (3/5). This gives ...

  S = 12/(1 -3/5) = 12·5/2 = 30

The series is convergent and has a sum of 30.