V. Let f(x) be a differentiable function such that for all æ > 1, • f(x) > 1, • f'(x) < f(x) and lim f(x) = 1. E ^(-1)" An) is conditionally convergent. Show that the series n=1

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter5: Graphs And The Derivative
Section5.3: Higher Derivatives, Concavity, And The Second Derivative Test
Problem 61E
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V. Let f(x) be a differentiable function such that for all x > 1,
f(x)
• f(x) > 1,
f'(x) <
and
• lim f(x) = 1.
Show that the series >(-1)"
f(n)
is conditionally convergent.
n=1
Transcribed Image Text:V. Let f(x) be a differentiable function such that for all x > 1, f(x) • f(x) > 1, f'(x) < and • lim f(x) = 1. Show that the series >(-1)" f(n) is conditionally convergent. n=1
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