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)
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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Equations and Inequations
Equations and inequalities describe the relationship between two mathematical expressions.
Linear Functions
A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.
Question
Solve.
![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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F670f70af-4732-487c-a000-2024d7bc94bd%2F7cdce961-a770-41dd-99e2-a57cf34c5227%2Fpf97wmk_processed.jpeg&w=3840&q=75)
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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