Let a₁0 be a real number (to be chosen below) and recursively define for n > 2. a. b. Let ai = an = .3 an-1+an-1 3 1. Show that 0 ≤ an ≤ (²)"−¹ for all n € N. Let a1 = 1 again. Show that lim an = 0. n→∞
Let a₁0 be a real number (to be chosen below) and recursively define for n > 2. a. b. Let ai = an = .3 an-1+an-1 3 1. Show that 0 ≤ an ≤ (²)"−¹ for all n € N. Let a1 = 1 again. Show that lim an = 0. 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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Question
Please prove the following step by step with focus on proof writing style
Transcribed Image Text:Let a₁0 be a real number (to be chosen below) and recursively define
an-1 + an-1
3
for n ≥ 2.
a.
b.
Let a1 =
Let a1 =
an
n-1
1. Show that 0 ≤ an ≤ (²)"−¹ for all n € N.
1 again. Show that lim an = 0.
n→∞
Expert Solution
Step 1: Using induction
Step by step
Solved in 3 steps with 3 images
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