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24. Define f: JJ by f(1) = 1, f(2)= 2, f(3) = 3, and f(n) = f(n-1) + f(n − 2) + f(n-3) for n ≥ 4. Prove that f(n) ≤ 2" for all n E J. 25. Define f : JJ by f(1) = 2 and, for n ≥ 2, f(n) = √3+ f(n - for all n E J. You may want to use your calculator for this exercise. 1). Prove that f(n) < 2.4

24. Define f: JJ by f(1) = 1, f(2)= 2, f(3) = 3, and f(n) = f(n-1) + f(n − 2) + f(n-3) for n ≥ 4. Prove that f(n) ≤ 2" for all n E J. 25. Define f : JJ by f(1) = 2 and, for n ≥ 2, f(n) = √3+ f(n - for all n E J. You may want to use your calculator for this exercise. 1). Prove that f(n) < 2.4

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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24. Define f: J→ J by f(1) = 1, f(2) = 2, f(3) = 3, and f(n) = f(n-1) + f(n − 2) + f(n-3) for n ≥ 4. Prove that f(n) ≤ 2" for all n EJ. 1 25. Define f: J→ J by f(1) = 2 and, for n ≥ 2, f(n) = V3 + f(n − 1). Prove that f(n) < 2.4 for all n E J. You may want to use your calculator for this exercise.
Transcribed Image Text:24. Define f: J→ J by f(1) = 1, f(2) = 2, f(3) = 3, and f(n) = f(n-1) + f(n − 2) + f(n-3) for n ≥ 4. Prove that f(n) ≤ 2" for all n EJ. 1 25. Define f: J→ J by f(1) = 2 and, for n ≥ 2, f(n) = V3 + f(n − 1). Prove that f(n) < 2.4 for all n E J. You may want to use your calculator for this exercise.
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