4. Do the following task. a. I :) State formally the definition of infinite series Σan in R. n=1 b. (. n=1 ) State formally when the infinite series an in R converge in terms of the limit of partial sum. Show that the series (−1)″−¹ = 1−1+1−1+1−1+…... C. n=1 1
4. Do the following task. a. I :) State formally the definition of infinite series Σan in R. n=1 b. (. n=1 ) State formally when the infinite series an in R converge in terms of the limit of partial sum. Show that the series (−1)″−¹ = 1−1+1−1+1−1+…... C. n=1 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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Number 4
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Transcribed Image Text:4. Do the following task.
a. I
;) State formally the definition of infinite series an in R.
n=1
b. (.
) State formally when the infinite series an in R converge in
terms of the limit of partial sum.
Show that the series (−1)″−¹ = 1−1+1−1+1−1+…..
C. (
n=1
1
n=1
diverge by showing that the limit of the partial sum sn = 1−1+...+(-1)^-1
does not exists.
Hint: Consider the subsequence {$2n} and {$2n-1} of the sequence {sn}.
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