Answered: n +1 | bartleby

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

See similar textbooks

Related questions

Question

How do you do the Alternating Series Test on this series and what is the result? Please show work so I can follow along.

Expert Solution

Step 1

Alternating series:

A series of the form

\sum _{n=0}^{\infty }(-1)^{n}a_{n}=a_{0}-a_{1}+a_{2}-a_{3}+\cdots \!

where either all a_n are positive or all a_n are negative, is called an alternating series.

The alternating series test then says: if $|a_{n}|$ decreases monotonically. and $\lim _{n\to \infty }a_{n}=0$ then the alternating series converges.

Moreover, let L denote the sum of the series, then the partial sum

S_{k}=\sum _{n=0}^{k}(-1)^{n}a_{n}\!

approximates L with error bounded by the next omitted term:

\left|S_{k}-L\right\vert \leq \left|S_{k}-S_{k+1}\right\vert =a_{k+1}.\!

Step by step

Solved in 2 steps with 5 images

Knowledge Booster

$Series$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

Similar questions