(10) Given the Taylor series f(z) = > a„(z – z,)" n=0 Find the Taylor series of the kth derivative (fk (2)) in sigma notation form in terms of n, k, z, zo, and a, .
(10) Given the Taylor series f(z) = > a„(z – z,)" n=0 Find the Taylor series of the kth derivative (fk (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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Need 9 and 10 please with correct options
![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 .](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8092a1cd-0dd2-4635-8c6a-c00b228c690a%2F466c28f0-f971-4d87-8734-f82fc09a0b13%2F19vnwyj_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 .
![11:04
4G 14 1 69%
Edit
f 88
50
In problems 6 – 9, choose the statement that applies to the series in the problem.
It is possible for an answer to be used more than once.
a) The series does not converge because the underlying sequence does not converge to zero.
b) The series does not converge because the series is a harmonic series.
c) The series does converge. It can be proven using either the ratio or the root test.
d) The series does converge but it cannot be proven using either the ratio or root test but it can
be proven using the alternating sign test.
e) The series does converge but it cannot be proven using the tools we have covered.
Problem 10: Find the absolute value of the 4th term of flk] (z) for the following:
am = m-3
k = 3
а) 33.286
b) 34.618
c) 36.003
d) 37,443
e) 38.940
z = 4
Zo = i
DO
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Transcribed Image Text:11:04
4G 14 1 69%
Edit
f 88
50
In problems 6 – 9, choose the statement that applies to the series in the problem.
It is possible for an answer to be used more than once.
a) The series does not converge because the underlying sequence does not converge to zero.
b) The series does not converge because the series is a harmonic series.
c) The series does converge. It can be proven using either the ratio or the root test.
d) The series does converge but it cannot be proven using either the ratio or root test but it can
be proven using the alternating sign test.
e) The series does converge but it cannot be proven using the tools we have covered.
Problem 10: Find the absolute value of the 4th term of flk] (z) for the following:
am = m-3
k = 3
а) 33.286
b) 34.618
c) 36.003
d) 37,443
e) 38.940
z = 4
Zo = i
DO
פם
Tools
Mobile View
Share
PDF to DOC
Edit on PC
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