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5 Let (sn) be a bounded sequence, and let k be a non number. onnegative real (a) Prove lim sup(ksn) = k · lim sup sn. (b) Do the same for lim inf. Hint: Use Exercise 11.8. (c) What happens in (a) and (b) if k < 0?

5 Let (sn) be a bounded sequence, and let k be a non number. onnegative real (a) Prove lim sup(ksn) = k · lim sup sn. (b) Do the same for lim inf. Hint: Use Exercise 11.8. (c) What happens in (a) and (b) if k < 0?

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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12.6 Let (sn) be a bounded sequence, and let k be a nonnegative real number. (a) Prove lim sup(ksn) = k · lim sup sn. (b) Do the same for lim inf. Hint: Use Exercise 11.8. (c) What happens in (a) and (b) if k < 0?
Transcribed Image Text:12.6 Let (sn) be a bounded sequence, and let k be a nonnegative real number. (a) Prove lim sup(ksn) = k · lim sup sn. (b) Do the same for lim inf. Hint: Use Exercise 11.8. (c) What happens in (a) and (b) if k < 0?
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