Consider the series 8 (-1)+1 √3n+2 (a) Show that this series converges using the Alternating Series Test. N (b) Find the smallest value of N for which the partial sum Sy=(-1)+1 of the series with an error of at most 1 10' n=1 √3n+2 approximates the value
Consider the series 8 (-1)+1 √3n+2 (a) Show that this series converges using the Alternating Series Test. N (b) Find the smallest value of N for which the partial sum Sy=(-1)+1 of the series with an error of at most 1 10' n=1 √3n+2 approximates the value
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
Question 2 full and q3(a) please!
![Math 152
Week 11 Workshop Problems
3/27/24
Write up your solutions to each of these problems on a seperate sheet of
paper.
1. For each of the following series determine if they converge or diverge. If they converge, do they converge
conditionally or converge absolutely?
(a) (-1)"(√n+1-√√n)
n=3
(b)
cos(n)
7
2. Consider the series
(-1)+1
√√3n+2
(a) Show that this series converges using the Alternating Series Test.
N
(b) Find the smallest value of N for which the partial sum SN =
(-1)+1
√√3n+2
approximates the value
n=1
of the series with an error of at most
10
3. Find the radius of convergence and interval of convergence for each of the following power series.
(a)(2
n=1
n" (x-7)"
n!
(b)
n=1
(5x + 2)²n
4"√n+1
4. If the power series Σan(x+2)" converges when x=-5, must it also converge when x = 2? Why or
why not?
n=0](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F509c3203-dcd1-467b-a86a-01689d0ddd27%2Febabe07b-ab35-4558-9d0c-ecf929b37926%2Fdsj8i1s_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Math 152
Week 11 Workshop Problems
3/27/24
Write up your solutions to each of these problems on a seperate sheet of
paper.
1. For each of the following series determine if they converge or diverge. If they converge, do they converge
conditionally or converge absolutely?
(a) (-1)"(√n+1-√√n)
n=3
(b)
cos(n)
7
2. Consider the series
(-1)+1
√√3n+2
(a) Show that this series converges using the Alternating Series Test.
N
(b) Find the smallest value of N for which the partial sum SN =
(-1)+1
√√3n+2
approximates the value
n=1
of the series with an error of at most
10
3. Find the radius of convergence and interval of convergence for each of the following power series.
(a)(2
n=1
n" (x-7)"
n!
(b)
n=1
(5x + 2)²n
4"√n+1
4. If the power series Σan(x+2)" converges when x=-5, must it also converge when x = 2? Why or
why not?
n=0
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