Show that for each p > 1, nP n=1 р—1 Hint: In class we showed that if a sequence {an}, and a function f satisfy the conditions of the Integral Test, then for each positive integer n=1 п, Sn < aj + f(x) dx, where s, is the nth partial sum of the series -1 an .

Show that for each p > 1, nP n=1 р—1 Hint: In class we showed that if a sequence {an}, and a function f satisfy the conditions of the Integral Test, then for each positive integer n=1 п, Sn < aj + f(x) dx, where s, is the nth partial sum of the series -1 an .

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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Question

Sequences and Series

Show that for each p > 1,
1
n=1
Hint: In class we showed that if a sequence {an } and a function f satisfy the conditions of the Integral Test, then for each positive integer
n=1
п,
n
Sn < aj +
f(x) dx,
where
Sn
is the nth partial sum of the series E an.
in=1

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