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1. Write out the following sequences: (a) an = 4n+1 (b) an = (-1)" (n³), n ≥ 0 (c) an = Q₁ = 4(1)+1 = 4+1 -5 5,9,13.. (-1)+12n 2n + 1 " n 1 (d) an = 1+ (-1)" (2n-1), n ≥ 1

1. Write out the following sequences: (a) an = 4n+1 (b) an = (-1)" (n³), n ≥ 0 (c) an = Q₁ = 4(1)+1 = 4+1 -5 5,9,13.. (-1)+12n 2n + 1 " n 1 (d) an = 1+ (-1)" (2n-1), n ≥ 1

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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Write out the sequences:
1. Write out the following sequences: (a) an = 4n+ 1 (b) an = (-1)" (n³), n ≥ 0 (c) an = Q₁ = 4(1)+1 = 441 = 5 (-1)"+¹2n 2n + 1 - n1 Q2 = 412) +1 = 8+1 93= 4(3) +1²= 12+ 13 (5,9,13...) (d) an = 1+ (-1)" (2n − 1), n ≥ 1 2. Prove: Proposition: If n E N, then 1 + (-1)" (2n-1) is a multiple of 4. rove: Proposition. Every multiple of 4 equals 1+ (-1)" (2n-1) for some
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 = 441 = 5 (-1)"+¹2n 2n + 1 - n1 Q2 = 412) +1 = 8+1 93= 4(3) +1²= 12+ 13 (5,9,13...) (d) an = 1+ (-1)" (2n − 1), n ≥ 1 2. Prove: Proposition: If n E N, then 1 + (-1)" (2n-1) is a multiple of 4. rove: Proposition. Every multiple of 4 equals 1+ (-1)" (2n-1) for some
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