Use mathematical induction to prove the following statements.(a) 4 is a factor of 9n − 5n for all integers n ≥ 1.(b) (1 1)n (1 n) (0 1) = (0 1) for all integers n ≥ 1.(c) If (tn) is a sequence defined recursively by t1 = 1; tn = 3t n-1+ 4,n ≥2,then tn = 3n-2 for all integers n ≥ 1.

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Description: Use mathematical induction to prove the following statements.(a) 4 is a factor of 9n − 5n for all integers n ≥ 1.(b) (1 1)n (1 n) (0 1) = (0 1) for all integers n ≥ 1.(c) If (tn) is a sequence defined recursive

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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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Use mathematical induction to _prove the following statements.

(a) 4 is a factor of 9ⁿ − 5ⁿfor all integers n ≥ 1.

(b) (1 1)ⁿ(1 n)

(0 1) = (0 1)
for all integers n ≥ 1.

n ≥2,then t_n = 3ⁿ-2 for all integers n ≥ 1.

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