Let (an) 1 and (bn)-1 be two sequences of real numbers. Prove or disprove each of the following statements: (a) ( 1) If the sequence (an)n-1 is defined by the recursive formula an+1 = -2-a, a₁ = 1, then (an)n-1 converges. =1 (b) (-_ -) If an exist, then lim (an-bn) 0. 81x bn for every n N and lim an and lim bn do not 84x 84x (c) ( -) If for every sequence of real numbers (cn) for which lim Cn does not exist, we have lim (an+cn) does not exist, then 818 81x lim an exists. 818

Let (an) 1 and (bn)-1 be two sequences of real numbers. Prove or disprove each of the following statements: (a) ( 1) If the sequence (an)n-1 is defined by the recursive formula an+1 = -2-a, a₁ = 1, then (an)n-1 converges. =1 (b) (-_ -) If an exist, then lim (an-bn) 0. 81x bn for every n N and lim an and lim bn do not 84x 84x (c) ( -) If for every sequence of real numbers (cn) for which lim Cn does not exist, we have lim (an+cn) does not exist, then 818 81x lim an exists. 818

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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