By hand solution neededHundred percent efficiency neededBy Hand solution needed in the order to get positive feedback please show me neat and clean work for it 5. Let (an) and (bn)-1 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 formulaan+1 = -2-a, a₁ = 1, then (an)=1 converges.(b) (^_ a) If anexist, then limn4x(c) {-) If for every sequence of real numbers (Cn)1 for whichlim Cn does not exist, we have lim (an+Cn) does not exist, then818n4xlim an exists.81x(d) (-- .bn for every n N and lim an and lim bn do not(an-bn) 0.84x84xconverges.If lim (a2n-an) = 0, then the sequence (an)n=1848

“Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

(a) (². ¹) If the sequence (an) is defined by the recursive formula an+1 = -2-a, a₁ = 1, then (an)=1 converges. (b) (^_ 84x 84x -) If an bn for every n N and lim an and lim bn do not exist, then lim (an-bn) 0. 81x (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

(a) (². ¹) If the sequence (an) is defined by the recursive formula an+1 = -2-a, a₁ = 1, then (an)=1 converges. (b) (^_ 84x 84x -) If an bn for every n N and lim an and lim bn do not exist, then lim (an-bn) 0. 81x (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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Question

By hand solution needed Hundred percent efficiency needed By Hand solution needed in the order to get positive feedback please show me neat and clean work for it

5. Let (an) and (bn)-1 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
n4x
lim an exists.
81x
(d) (-- .
bn for every n N and lim an and lim bn do not
(an-bn) 0.
84x
84x
converges.
If lim (a2n-an) = 0, then the sequence (an)n=1
848

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