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

Let (a,) and (bn) be sequences in R and define c, as follows: For each natural number n, let c, = 5a, + 2b,. If (a,)is %3D 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 Ss' is the set of subsequential limits of (a,).

Let (a,) and (bn) be sequences in R and define c, as follows: For each natural number n, let c, = 5a, + 2b,. If (a,)is %3D 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 Ss' is the set of subsequential limits of (a,).

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.2: Arithmetic Sequences

Problem 64E

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Concept explainers

Matrices

‘Matrices’ is the plural form of the word matrix, and it is basically a spreadsheet in the form of a box. In mathematics, various functions can be carried out with matrices. Generally, a matrix comes in the shape of a square or rectangle. The elements are distributed horizontally in the form of rows, and vertically in the form of columns.

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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,).

Branch of mathematical analysis that studies real numbers, sequences, and series of real numbers and real functions. The concepts of real analysis underpin calculus and its application to it. It also includes limits, convergence, continuity, and measure theory.

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