Please Don't write details, just give me the final answer as quick as possible.Also, please write your email, I want ask you on Real analysis and I will pay you for each question you can help me do it. Let (a,) and (bn) be sequences in R and define c, as follows: For each natural number n, let c, = 5a, + 2bn. If (a,)isconvergent:Select one:O a. and (b,) converges to 0, then (c,-5a,) is eventually a constant sequence.O b. then (b,) is bounded if and only if (c,) is bounded.O c. none of the listed statements is true.O d. then sup (S)= inf(S') where s' is the set of subsequential limits of (a,).

Given an is convergent So an is bounded since any convergent sequence is bounded

Answered: Let (a,) and (bn) be sequences in R and…

Advanced Engineering Mathematics

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Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

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Please Don't write details, just give me the final answer as quick as possible. Also, please write your email, I want ask you on Real analysis and I will pay you for each question you can help me do it.

Let (a,) and (bn) be sequences in R and define c, as follows: For each natural number n, let c, = 5a, + 2bn. If (a,)is
convergent:
Select one:
O a. and (b,) converges to 0, then (c,-5a,) is eventually a constant sequence.
O b. then (b,) is bounded if and only if (c,) is bounded.
O c. none of the listed statements is true.
O d. then sup (S)= inf(S') where s' is the set of subsequential limits of (a,).

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