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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
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 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
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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