Prove that the function 1 f: (1, co) → R, x + n=1 is infinitely differentiable. (Do this by showing that the series, and all its derivatives, are uniformly convergent on (a, ∞) for any fixed a > 1, and appeal to the relevant theorems. ) -

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter2: Equations And Inequalities
Section2.1: Equations
Problem 75E
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Prove that the function
00
f: (1, co) → R, x >
Σ
n=1
is infinitely differentiable. (Do this by showing that the series, and all its derivatives, are uniformly
convergent on (a, 0) for any fixed a > 1, and appeal to the relevant theorems. )
Transcribed Image Text:Prove that the function 00 f: (1, co) → R, x > Σ n=1 is infinitely differentiable. (Do this by showing that the series, and all its derivatives, are uniformly convergent on (a, 0) for any fixed a > 1, and appeal to the relevant theorems. )
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