Question

Problem 14

Answer 1

Given information

Given series is  

Step-by-step explanation

Step 1.

Alternating Series Estimation Theorem:- If  is the sum of an alternating series that satisfies

  Then the series is convergent and  

The series is For series convergent use alternating series test 

Here, Then  

 

Therefore, by this it can be said that the given series is convergent.

Step 2:

For sum to the indicated accuracy use alternating series estimation

 

Notice that and  

By the alternating series estimation theorem then

 

This error of less than does not affect the third decimal place,

Therefore correct to three decimal places.