   Chapter 11.4, Problem 34E

Chapter
Section
Textbook Problem

Use the sum of the first 10 terms to approximate the sum of the series. Estimate the error. ∑ n − 1 ∞ e 1 / n n 4

To determine

To approximate:

i) The sum of the first ten terms of the series and

ii) To estimate the error.

Explanation

1) Concept:

The remainder estimate for the integral test:

Suppose fk=ak where f  is a continuous positive decreasing functions for n, and an is convergent. If  Rn=s-sn, then n+1fxdxRnnfxdx

The error can be calculated by using the concept

RnTnn1xndx

Where Rn=s-sn=an+1+an+2+

And Tn=t-tn=bn+1+bn+2+

Here  anbn therefore RnTn ,     bn is p-series

2) Given:

n=1e1nn4

3) Calculation:

The given series is n=1e1nn4

The first ten terms are

n=110e1/nn4=e11+e0

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