Geometric series Evaluate the geometric series

Chapter 11, Problem 20E

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QUESTION:

19-34. Geometric series Evaluate the geometric series or state that it diverges.

\(\sum_{k=0}^{\infty}\left(\frac{3}{5}\right)^{k}\)

Questions & Answers

QUESTION:

19-34. Geometric series Evaluate the geometric series or state that it diverges.

\(\sum_{k=0}^{\infty}\left(\frac{3}{5}\right)^{k}\)

ANSWER:

Problem 20E

Geometric series Evaluate the geometric series or state that it diverges.

Solution

Step 1

In this problem we have to evaluate the geometric series  or we have to state that it diverges.

The sum of an infinite Geometric series  is given by if  .

We have

Here and

Hence  the sum ofis

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