5. The subsequence of (xn) = () is.. a) (1층..) 0) (1.층,급.) b) (1,1,1, ..) a) (1.-) 6. The sequence (xn) = (3,3,3,3, ...) is... a) not Cauchy b) unbounded c) divergent d) convergent Question 2 A) If (xn) is a decreasing and bounded sequence. Prove that (xn) is convergent with lim xn = inf {xn :n E N} 1 B) By using (A), Find lim n0 yn C) Prove that a Cauchy sequence of real numbers is bounded.

5. The subsequence of (xn) = () is.. a) (1층..) 0) (1.층,급.) b) (1,1,1, ..) a) (1.-) 6. The sequence (xn) = (3,3,3,3, ...) is... a) not Cauchy b) unbounded c) divergent d) convergent Question 2 A) If (xn) is a decreasing and bounded sequence. Prove that (xn) is convergent with lim xn = inf {xn :n E N} 1 B) By using (A), Find lim n0 yn C) Prove that a Cauchy sequence of real numbers is bounded.

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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