(e) Show that every n ≥ 8 can be written as 3a+5b for some a, b € N.
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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Part e please
Transcribed Image Text:2. Prove the following, using induction:
(a) If an+1 = an/(an +1) prove that an = ao/(nao+1) for all n ≥ 0.
(b) Define fo = 0, f₁ = 1 and fn = fn-1 + fn-2 for n ≥ 2. Show that
3 fak for all k ≥ 0.
(c) Show that for 2" > 4n for n > 5.
(d) Show that 3 | 5
- 2" for all n.
(e) Show that every
n ≥ 8 can be written as 3a+5b for some a, b € N.
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