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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 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,).

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 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,).

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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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 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,).
Transcribed Image Text: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 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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