00 (10) Given the Taylor series f(2) = a,(z – za)" n=0 Find the Taylor series of the kth derivative (flk| (2)) in sigma notation form in terms of n, k, z, zo, and a, .
00 (10) Given the Taylor series f(2) = a,(z – za)" n=0 Find the Taylor series of the kth derivative (flk| (2)) in sigma notation form in terms of n, k, z, zo, and a, .
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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I need 10 and then 9
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(3)
Z, = (-1)"-k +201, where k is any integer.
(4) zn = n² +/n2
(5)
Zn = (5 – 41)"
In problems 6 - 10, determine if the given series is convergent.
Use ratio test, alternating series test, etc.
S= En=0 2
Hint: split the series into 2 series
(6)
(7)
S=En=0 (3n+1)!
(-1)"(1+1)3n
(8)
S= En=0
(n)!
(9)
S = E=1
Hint: split the series into 2 (or more) series
(10) Given the Taylor series f(z) =
a„(z – zo)"
Find the Taylor series of the kth derivative (flk] (z)) in sigma notation form
in terms of n, k, z, zo, and an .](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbfa81757-91da-4bc7-9c33-ab5103c96f36%2F25483488-78a0-4ec0-8581-40b500db0cf8%2F3l38i1a_processed.jpeg&w=3840&q=75)
Transcribed Image Text:101
(3)
Z, = (-1)"-k +201, where k is any integer.
(4) zn = n² +/n2
(5)
Zn = (5 – 41)"
In problems 6 - 10, determine if the given series is convergent.
Use ratio test, alternating series test, etc.
S= En=0 2
Hint: split the series into 2 series
(6)
(7)
S=En=0 (3n+1)!
(-1)"(1+1)3n
(8)
S= En=0
(n)!
(9)
S = E=1
Hint: split the series into 2 (or more) series
(10) Given the Taylor series f(z) =
a„(z – zo)"
Find the Taylor series of the kth derivative (flk] (z)) in sigma notation form
in terms of n, k, z, zo, and an .
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