Question

a) Prove or disprove that whenever $n \ge 3$, $f_n > a^{n-2}$, where $a = (1 + \sqrt{5}) / 2$ using strong induction principle.

Name: a) Prove or disprove that whenever n ≥ 3, fn > a^n-2, where a = (1 + √(5)) / 2 using strong induction principle.
Uploaded: 2023-11-21T07:27:39-08:00
Duration: 2 min 31 s
Channel: Adi S
Description: a) Prove or disprove that whenever n ≥ 3, fn > a^n-2, where a = (1 + √(5)) / 2 using strong induction principle.

          a) Prove or disprove that whenever $n \ge 3$, $f_n > a^{n-2}$, where $a = (1 + \sqrt{5}) / 2$ using strong induction principle.

Added by Denise R.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Adi S

11/21/2023

Step 1

Step 1: Base case for n ≤ 3 When n = 1, f(1) = 1 > a^(1-2) = a^(-1) = 1/a = 1/(1 + √5)/2 = 2/(1 + √5) > 1 When n = 2, f(2) = 1 > a^(2-2) = a^0 = 1 When n = 3, f(3) = 2 > a^(3-2) = a^1 = (1 + √5)/2 Show more…

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a) Prove or disprove that whenever n is less than or equal to 3, f(n) > a^(n-2), where a = (1 + √5)/2 using strong induction principle. Prove or disprove that whenever n > 3, f > a - where a = 1 + 5/2 using strong induction principle.