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3. The alternating series test can be used to show convergence for which of the following series? I. 1 II. sin 1 1 + 16. sin 3 + an + .., where an = (-1)"+1 9. sin 2 4 25 sin 4 n2 sin 6 + 36 + bn +.., where b, = (-1)"+1 sin n + Cn +:., sin 5 ... %3D 16 25 1 n2 9 1 III. V2+1 1 + V3+1 +... V2–1 V3-1 V4+1 V4–1 if n = 2k – 1 Vk+1+1 where cn = if n = 2k Vk+1–1 (A) I only П only I and II only (В) (C) (D) I and III only

3. The alternating series test can be used to show convergence for which of the following series? I. 1 II. sin 1 1 + 16. sin 3 + an + .., where an = (-1)"+1 9. sin 2 4 25 sin 4 n2 sin 6 + 36 + bn +.., where b, = (-1)"+1 sin n + Cn +:., sin 5 ... %3D 16 25 1 n2 9 1 III. V2+1 1 + V3+1 +... V2–1 V3-1 V4+1 V4–1 if n = 2k – 1 Vk+1+1 where cn = if n = 2k Vk+1–1 (A) I only П only I and II only (В) (C) (D) I and III only

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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3. The alternating series test can be used to show convergence for which of the following series? (-1)*+1 ! where b, = (-1)"+1. + Cn + I. 1-+ - 1s + where an + an +. sin 6 36 | n2 36 sin 4 16 25 sin 2 sin 3 sin 5 sin n П. sin + bn + ... 1 4 1 1 25 1 1 n2 V3-1 1 + V4-1 III. V2+1 V2-1 V3+1 V4+1 1 if n 2k – 1 k+1+1 where Cn 1 if n = 2k Vk+1–1 (A) I only (В) П only (C) I and II only (D) I and III only
Transcribed Image Text:3. The alternating series test can be used to show convergence for which of the following series? (-1)*+1 ! where b, = (-1)"+1. + Cn + I. 1-+ - 1s + where an + an +. sin 6 36 | n2 36 sin 4 16 25 sin 2 sin 3 sin 5 sin n П. sin + bn + ... 1 4 1 1 25 1 1 n2 V3-1 1 + V4-1 III. V2+1 V2-1 V3+1 V4+1 1 if n 2k – 1 k+1+1 where Cn 1 if n = 2k Vk+1–1 (A) I only (В) П only (C) I and II only (D) I and III only
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