Homework Help is Here – Start Your Trial Now!
Math
Calculus
THEOREM 10.18 Remainder in Alternating Series 00 Let 2(-1)*+'a, be a convergent alternating series with terms that are nonin- k=1 creasing in magnitude. Let R, = S – S, be the remainder in approximating the value of that series by the sum of its first n terms. Then |R, < a,+ 1. In other words, the magnitude of the remainder is less than or equal to the magnitude of the first neglected term. (-1)* Σ ;n = 5 O k + k2 + 1 k=0

THEOREM 10.18 Remainder in Alternating Series 00 Let 2(-1)*+'a, be a convergent alternating series with terms that are nonin- k=1 creasing in magnitude. Let R, = S – S, be the remainder in approximating the value of that series by the sum of its first n terms. Then |R, < a,+ 1. In other words, the magnitude of the remainder is less than or equal to the magnitude of the first neglected term. (-1)* Σ ;n = 5 O k + k2 + 1 k=0

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.1: Infinite Sequences And Summation Notation
Problem 72E
See similar textbooks
icon
Related questions
Question

For the following convergent alternating series, evaluate the nth partial sum for the given value of n. Then use Theorem 10.18 to find an upper bound for the error | S - Sn | in using the nth partial sum Sn to estimate the value of the series S.

THEOREM 10.18 Remainder in Alternating Series 00 Let 2(-1)*+'a, be a convergent alternating series with terms that are nonin- k=1 creasing in magnitude. Let R, = S – S, be the remainder in approximating the value of that series by the sum of its first n terms. Then |R, < a,+ 1. In other words, the magnitude of the remainder is less than or equal to the magnitude of the first neglected term.
Transcribed Image Text:THEOREM 10.18 Remainder in Alternating Series 00 Let 2(-1)*+'a, be a convergent alternating series with terms that are nonin- k=1 creasing in magnitude. Let R, = S – S, be the remainder in approximating the value of that series by the sum of its first n terms. Then |R, < a,+ 1. In other words, the magnitude of the remainder is less than or equal to the magnitude of the first neglected term.
(-1)* Σ ;n = 5 O k + k2 + 1 k=0
Transcribed Image Text:(-1)* Σ ;n = 5 O k + k2 + 1 k=0
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 4 steps with 4 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
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.
Recommended textbooks for you
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
SEE MORE TEXTBOOKS