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(d) (--. converges. If lim (a2n-an) = 0, then the sequence (an)n=1 84x

(d) (--. converges. If lim (a2n-an) = 0, then the sequence (an)n=1 84x

Advanced Engineering Mathematics
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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D part needed by Hand solution Kindly solve part D in the order to get positive feedback please show me neat and clean work for it by hand solution needed
5. Let (an) and (bn) be two sequences of real numbers. Prove or disprove each of the following statements: (a) (*. 7) If the sequence (an)n-1 is defined by the recursive formula an+1 = -2-a, a₁ = 1, then (an)=1 converges. (b) (^_ a) If an exist, then lim n4x (c) { -) If for every sequence of real numbers (Cn)1 for which lim Cn does not exist, we have lim (an+cn) does not exist, then 818 lim an exists. 81x (d) (-- . bn for every n e N and lim an and lim bn do not (an-bn) 0. 84x 84x converges. 848 If lim (a2n-an) = 0, then the sequence (an)n=1 84x
Transcribed Image Text:5. Let (an) and (bn) be two sequences of real numbers. Prove or disprove each of the following statements: (a) (*. 7) If the sequence (an)n-1 is defined by the recursive formula an+1 = -2-a, a₁ = 1, then (an)=1 converges. (b) (^_ a) If an exist, then lim n4x (c) { -) If for every sequence of real numbers (Cn)1 for which lim Cn does not exist, we have lim (an+cn) does not exist, then 818 lim an exists. 81x (d) (-- . bn for every n e N and lim an and lim bn do not (an-bn) 0. 84x 84x converges. 848 If lim (a2n-an) = 0, then the sequence (an)n=1 84x
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