1. Use any method to determine whether the following series converges or dive (a) E(-1)" n=1 (-1)"+1 (b) E (n+ 1) In(n + 1)

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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1. Use any method to determine whether the following series converges or diverges.
(n) E(-1)"#
n=1
(-1)"+1
(0) 2 (n + 1) In(n + 1)
sin
2. Determine if the series
2
is absolutely or conditionally convergent
(r – 3)"
2" +1
3. Determine the interval of convergence of
n=1
4. Consider the function defined by
f(x) = log3(2r – 1).
Determine the Taylor series expansion about a = 1.
Transcribed Image Text:1. Use any method to determine whether the following series converges or diverges. (n) E(-1)"# n=1 (-1)"+1 (0) 2 (n + 1) In(n + 1) sin 2. Determine if the series 2 is absolutely or conditionally convergent (r – 3)" 2" +1 3. Determine the interval of convergence of n=1 4. Consider the function defined by f(x) = log3(2r – 1). Determine the Taylor series expansion about a = 1.
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