(-1)"x2n+1 2n +1

Algebra: Structure And Method, Book 1
(REV)00th Edition
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Chapter3: Solving Equation And Problems
Section3.4: Using Equations To Solve Problems
Problem 32P
icon
Related questions
Question

find the interval of convergence of the power series. (Be sure to include a check for convergence at the endpoints of the interval.)

(-1)"x²n+1
.ゾ
2n +1
n=0
Transcribed Image Text:(-1)"x²n+1 .ゾ 2n +1 n=0
A ball is dropped from a height of 16 feet. Each time it drops h feet, it rebounds 0.81h feet. The ball takes the following times for each fall.
S1 = 0 when t = 1
= 0 when t = 0.9
S1 = -16t + 16,
s2 = -16t + 16(0.81),
S3 = -16t + 16(0.81)2,
S4 = -16 + 16(0.81)³,
S2
= 0 when t = (0.9)2
S4 = 0 whent = (0.9)3
S3
%3D
Sn = -162 + 16(0.81)" - 1,
= 0 when t = (0.9)" - 1
Sn
Beginning with s2, the ball takes the same amount of time to bounce up as it does to fall, and so the total time elapsed before it comes to rest is given by
t = 1 + 2 ) (0.9)".
n = 1
Find this total time.
t =
sec
Transcribed Image Text:A ball is dropped from a height of 16 feet. Each time it drops h feet, it rebounds 0.81h feet. The ball takes the following times for each fall. S1 = 0 when t = 1 = 0 when t = 0.9 S1 = -16t + 16, s2 = -16t + 16(0.81), S3 = -16t + 16(0.81)2, S4 = -16 + 16(0.81)³, S2 = 0 when t = (0.9)2 S4 = 0 whent = (0.9)3 S3 %3D Sn = -162 + 16(0.81)" - 1, = 0 when t = (0.9)" - 1 Sn Beginning with s2, the ball takes the same amount of time to bounce up as it does to fall, and so the total time elapsed before it comes to rest is given by t = 1 + 2 ) (0.9)". n = 1 Find this total time. t = sec
Expert Solution
steps

Step by step

Solved in 3 steps with 2 images

Blurred answer
Knowledge Booster
Power 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: Structure And Method, Book 1
Algebra: Structure And Method, Book 1
Algebra
ISBN:
9780395977224
Author:
Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:
McDougal Littell
Elementary Algebra
Elementary Algebra
Algebra
ISBN:
9780998625713
Author:
Lynn Marecek, MaryAnne Anthony-Smith
Publisher:
OpenStax - Rice University
Algebra for College Students
Algebra for College Students
Algebra
ISBN:
9781285195780
Author:
Jerome E. Kaufmann, Karen L. Schwitters
Publisher:
Cengage Learning
Intermediate Algebra
Intermediate Algebra
Algebra
ISBN:
9781285195728
Author:
Jerome E. Kaufmann, Karen L. Schwitters
Publisher:
Cengage Learning
College Algebra
College Algebra
Algebra
ISBN:
9781938168383
Author:
Jay Abramson
Publisher:
OpenStax
Big Ideas Math A Bridge To Success Algebra 1: Stu…
Big Ideas Math A Bridge To Success Algebra 1: Stu…
Algebra
ISBN:
9781680331141
Author:
HOUGHTON MIFFLIN HARCOURT
Publisher:
Houghton Mifflin Harcourt