15. Let {fn} be a sequence on C([a, b]). Assume that fn (x) 2 fn+1(x) for all x E [a, b]. Show that each fn are integrable on [a, b]. Show also that there is an integrable function f: [a, b] → R such that for every e > 0, there is a natural number N so that if n > N, then || (n (x) – f(x))dx|< e

15. Let {fn} be a sequence on C([a, b]). Assume that fn (x) 2 fn+1(x) for all x E [a, b]. Show that each fn are integrable on [a, b]. Show also that there is an integrable function f: [a, b] → R such that for every e > 0, there is a natural number N so that if n > N, then || (n (x) – f(x))dx|< e

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 72E

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