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Suppose real sequences (sn) and (tn) are bounded. (That is, that their ranges are bounded sets.) i. Show the sequence given by (sn + tn) is bounded. ii. For any real number α, show that the sequence (α⋅sn) is bounded.

Suppose real sequences (sn) and (tn) are bounded. (That is, that their ranges are bounded sets.) i. Show the sequence given by (sn + tn) is bounded. ii. For any real number α, show that the sequence (α⋅sn) is bounded.

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. Suppose real sequences (sn) and (tn) are bounded. (That is, that their ranges are bounded sets.)
i. Show the sequence given by (sn + tn) is bounded.
ii. For any real number α, show that the sequence (α⋅sn) is bounded.

D. Suppose real sequences (sn) and (tn) are bounded. (That is, that their ranges are bounded sets.) i. Show the sequence given by (Sn + tn) is bounded. ii. For any real number x, show that the sequence (a.s) is bounded.
Transcribed Image Text:D. Suppose real sequences (sn) and (tn) are bounded. (That is, that their ranges are bounded sets.) i. Show the sequence given by (Sn + tn) is bounded. ii. For any real number x, show that the sequence (a.s) is bounded.
Expert Solution
Step 1

We know the definition of bounded sequence,

A real sequence an is said to be bounded sequence if there exists a real number a, b such that a≤an≤b , ∀n∈ℕ.

We have given that sn and tn are bounded sequence.

Therefore there exists a real numbers p, q, r, s such that, p≤sn≤q and r≤tn≤s ∀n≥ℕ.

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