1. Determine whether the following series converge. Rigorously justify your answers (using the convergence tests from the lecture). 2n 2n (a) (b) Σ n! n=1 1+ 2n n=0 n=1
1. Determine whether the following series converge. Rigorously justify your answers (using the convergence tests from the lecture). 2n 2n (a) (b) Σ n! n=1 1+ 2n n=0 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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![n=0 \m=0
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b Answered: H1. Find the solution to the...
1. Determine whether the following series converge. Rigorously justify your answers
(using the convergence tests from the lecture).
n
2n
2n
(a)
Σ
(b)
(c)
n² + 1
n=1
п!
n=1
1+ 2n'
n=0
(f) £(-1)n+1[sin n|
n4
n2
1
(d)
(e)
n4 + 1
n=1
Зп + 2
n=1
n=1
n!
1
Σ
(h) ΣΙΣ
(2n)!
2m
n=1
2. [Python question: submit a print-out of your answer]
We have shown that the harmonic series E diverges because its sequence of
1
'n=l n
partial sums
k
1
Sk =
n
n=1
is unbounded above. Hence, given any M e R, there exists some k e N such that
> M. By experimenting with Python, find the smallest k E N such that
Sk
a) sk > 4,
(b) Sk > 8,
(c) Sk > 12,
(d) sk > 16.
A
4,621
FEB
27
W
lil O](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F986f6c25-9d5d-4e3f-93bc-35b073c4428b%2F950fec9a-cd98-4e79-bb2e-7d312daff0bf%2Fmt51z7_processed.png&w=3840&q=75)
Transcribed Image Text:n=0 \m=0
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100% 4A
Sun 20:03
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X Bb https://learn-eu-central-1-prod-fleet01...
b Answered: H1. Find the solution to the...
1. Determine whether the following series converge. Rigorously justify your answers
(using the convergence tests from the lecture).
n
2n
2n
(a)
Σ
(b)
(c)
n² + 1
n=1
п!
n=1
1+ 2n'
n=0
(f) £(-1)n+1[sin n|
n4
n2
1
(d)
(e)
n4 + 1
n=1
Зп + 2
n=1
n=1
n!
1
Σ
(h) ΣΙΣ
(2n)!
2m
n=1
2. [Python question: submit a print-out of your answer]
We have shown that the harmonic series E diverges because its sequence of
1
'n=l n
partial sums
k
1
Sk =
n
n=1
is unbounded above. Hence, given any M e R, there exists some k e N such that
> M. By experimenting with Python, find the smallest k E N such that
Sk
a) sk > 4,
(b) Sk > 8,
(c) Sk > 12,
(d) sk > 16.
A
4,621
FEB
27
W
lil O
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