Let (Jn)neN be a sequence of functions f: R → R satisfying |fn+1(c) – fn(c)|< a\fn(c) – fn-1(c)[for n > 2 and neN , and ae(0, 1). Prove that (Sn)n€N is a pointwise convergent sequence of functions at x = c.
Let (Jn)neN be a sequence of functions f: R → R satisfying |fn+1(c) – fn(c)|< a\fn(c) – fn-1(c)[for n > 2 and neN , and ae(0, 1). Prove that (Sn)n€N is a pointwise convergent sequence of functions at x = c.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.1: Infinite Sequences And Summation Notation
Problem 36E
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