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(b) Prove that, for all positive integers n, a-3-1-2", steps step 1: step 2: step 3: step 4: step 5: step 6: final step: reasoning base step inductive hypothesis using recursive definition for k+ 1 term using inductive hypothesis distribute 6 and note that 6=2×3 factor out factor out 2²

(b) Prove that, for all positive integers n, a-3-1-2", steps step 1: step 2: step 3: step 4: step 5: step 6: final step: reasoning base step inductive hypothesis using recursive definition for k+ 1 term using inductive hypothesis distribute 6 and note that 6=2×3 factor out factor out 2²

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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(b) Prove that, for all positive integers n, an = 3n-¹ – 2n. steps step 1: step 2: step 3: step 4: step 5: step 6: final step: reasoning base step inductive hypothesis using recursive definition for k + 1 term using inductive hypothesis distribute 6 and note that 6=2×3 factor out 3k-1 factor out 2k
Transcribed Image Text:(b) Prove that, for all positive integers n, an = 3n-¹ – 2n. steps step 1: step 2: step 3: step 4: step 5: step 6: final step: reasoning base step inductive hypothesis using recursive definition for k + 1 term using inductive hypothesis distribute 6 and note that 6=2×3 factor out 3k-1 factor out 2k
7. n ≥ 3. (a) Write the next two terms of the sequence. a3 = Define a sequence {an} recursively by a₁ = −1 = a2, and an = 5an-1 - 6an-2 for all integers a4 = Part (b) of this problem is on the next page.
Transcribed Image Text:7. n ≥ 3. (a) Write the next two terms of the sequence. a3 = Define a sequence {an} recursively by a₁ = −1 = a2, and an = 5an-1 - 6an-2 for all integers a4 = Part (b) of this problem is on the next page.
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