   Chapter 9.4, Problem 49E Calculus: Early Transcendental Fun...

7th Edition
Ron Larson + 1 other
ISBN: 9781337552516

Solutions

Chapter
Section Calculus: Early Transcendental Fun...

7th Edition
Ron Larson + 1 other
ISBN: 9781337552516
Textbook Problem

Using a Series Consider the series ∑ n = 1 ∞ 1 ( 2 n − 1 ) 2 (a) Verify that the series convergence.(b) Use a graphing, utility in complete the table. n 5 10 20 50 100 S n (c) The sum of the series in π2/8. Find the sum of the series ∑ n = 3 ∞ 1 ( 2 n − 1 ) 2 (d) Use a graphing utility to find the sum of the series. ∑ n = 10 ∞ 1 ( 2 n − 1 ) 2

(a)

To determine

To Calculate: Verify that the given series converges.

Explanation

Given: The given series is n=11an=n=11(2n1)2

Calculation:

Let (2n1)=z

Then we can write the given series as

(b)

To determine

To Calculate: Compute the given table

 n 5 10 20 50 100 Sn

(c)

To determine

To Calculate: Find the sum of the series n=31(2n1)2

(d)

To determine

To Calculate: Find the sum of the series n=101(2n1)2

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