(b) an= (-1)" (n³), n ≥ 0 (c) an = (-1)+12n 2n +1: n #1 C (d) an = 1+ (-1)" (2n − 1), 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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How can we solve b, c, and d?
1. Write out the following sequences:
(a) an = = 4n+ 1
(b) an= (-1)" (n³), n ≥ 0
(c) an
=
Q₁ = 4(1+1 = 461
-5
5,9,13
(-1)"+12n
2n +1n1
(d) an = 1+ (-1)" (2n-1), n ≥ 1
2. Prove: Proposition: If n E N, then 1 + (-1)"
Case 1
n-ak, (-1) = (-1)*
1 + (-1) n (2n-1) = 1 + (₁)
multiple of 4
4k ts
Case 3
Transcribed Image Text:1. Write out the following sequences: (a) an = = 4n+ 1 (b) an= (-1)" (n³), n ≥ 0 (c) an = Q₁ = 4(1+1 = 461 -5 5,9,13 (-1)"+12n 2n +1n1 (d) an = 1+ (-1)" (2n-1), n ≥ 1 2. Prove: Proposition: If n E N, then 1 + (-1)" Case 1 n-ak, (-1) = (-1)* 1 + (-1) n (2n-1) = 1 + (₁) multiple of 4 4k ts Case 3
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