Prove each of the following. (a) Given a real number a > 1 with a N, show that there is some natural number m € N such that m< a
Prove each of the following. (a) Given a real number a > 1 with a N, show that there is some natural number m € N such that m< a
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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Transcribed Image Text:Prove each of the following.
(a) Given a real number a > 1 with a N, show that there is some natural number m € N
such that
m< a <m+1
(b) Prove that 2m<m! + 2 for m € N.
(c) For any nonzero real number r, prove
71
I-
2²
i=1
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