   Chapter 11.5, Problem 31E

Chapter
Section
Textbook Problem

Is the 50th partial sum s 50 of the alternating series ∑ n = 1 ∞ ( − 1 ) n − 1 / n an overestimate or an underestimate of the total sum? Explain.

To determine

To estimate:

The partial sum   s50 of an alternating series is an overestimate or an underestimate.

Explanation

1) Concept:

Alternating Series Test:

If the alternating series

n=1-1nbn,  bn>0

satisfies,

i) bn+1<bn for all  n

ii) limnbn=0

then the series is convergent otherwise series is divergent.

The alternating series estimation theorem:

If   s=-1n-1bn, where   bn>0, is the sum of an alternating series that satisfies

i) bn+1bn and

ii) limnbn=0

then,

Rn=s-snbn

2) Given:

n=1-1n-1n

3) Calculation:

The given series is given as

n=0

Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

Find more solutions based on key concepts 