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 .
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.3: Geometric Sequences
Problem 82E
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Sequences and Series
Transcribed Image Text: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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