Question 1 ( a and b ) and q4 please!

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Question 1 ( a and b ) and q4 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
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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