Answered: 3. Prove that the sequence of functions…

3. Prove that the sequence of functions (fn)1 converges uniformly on X CR if and only if the series of functions f₁ + Σ(fn-fn-1) n=2 converges uniformly on X.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.3: Geometric Sequences

Problem 49E

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Question

Real analysis

3. Prove that the sequence of functions (fn)1 converges uniformly
on XCR if and only if the series of functions
f₁ + Σ(fn-fn-1)
converges uniformly on X.
n=2

Branch of mathematical analysis that studies real numbers, sequences, and series of real numbers and real functions. The concepts of real analysis underpin calculus and its application to it. It also includes limits, convergence, continuity, and measure theory.

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