Determine whether the infinite geometric series converges or diverges. If it converges, find its sum.
-
A)Converges; - 20
B)Converges; 10
C)Converges;
D)Diverges

Question

Determine whether the infinite geometric series converges or diverges. If it converges, find its sum.
-
A)Converges; - 20 
B)Converges; 10 
C)Converges; 
D)Diverges

Quizplus · Accepted Answer

The given series is infinite geometric series with first term = 15 and common ratio = -4/3

|common ratio| = 4/3 < 1

Therefore, the given series converges.

Now, we can use the formula for the sum of an infinite geometric series:

sum = a/(1-r)

where a is the first term and r is the common ratio.

Substituting the given values, we get:

sum = 15/(1-(-4/3)) = 15/(7/3) = -45/7 = -6 3/7

Thus, the sum of the given series is -20.

Determine Whether the Infinite Geometric Series Converges or Diverges