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1. Prove that for any n > 2, n E N, one has (1-)(--)(--) - (-) - n +1 2n

1. Prove that for any n > 2, n E N, one has (1-)(--)(--) - (-) - n +1 2n

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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1. Prove that for any n > 2, n E N, one has (1-:)(-)(- -)- (-) - n+1 ... 2n 2. Determine the supremum of the following set {Vn+1- Vn : n e N}. 3. Provide an example of a positive sequence (an) such that Van + 1 as n → o, but an+1/an does not tend to 1, as n → o. (clarifications: an > 0 for any n. The sequence an+1/an must not have limit 1 ; it can have a different limit or no limit at all).
Transcribed Image Text:1. Prove that for any n > 2, n E N, one has (1-:)(-)(- -)- (-) - n+1 ... 2n 2. Determine the supremum of the following set {Vn+1- Vn : n e N}. 3. Provide an example of a positive sequence (an) such that Van + 1 as n → o, but an+1/an does not tend to 1, as n → o. (clarifications: an > 0 for any n. The sequence an+1/an must not have limit 1 ; it can have a different limit or no limit at all).
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