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Prove that n + 2n is divisible by 3 for each n eN. Let z = sin 1 (in radians) and let y = v2. Prove that the following statement is false: (z+ y € Q) A (r- y e Q). Let a = 1 and let az = . For n 2 3, we define recursively an = an-2- an-1. Is it true that a2021 is rational? Prove that your answer is correct.

Prove that n + 2n is divisible by 3 for each n eN. Let z = sin 1 (in radians) and let y = v2. Prove that the following statement is false: (z+ y € Q) A (r- y e Q). Let a = 1 and let az = . For n 2 3, we define recursively an = an-2- an-1. Is it true that a2021 is rational? Prove that your answer is correct.

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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(a) Prove that n + 2n is divisible by 3 for each n EN. (b) Let z = sin 1 (in radians) and let y = v2. Prove that the following statement is false: (z+ y € Q) A (1- y E Q). (c) Let ai = 1 and let a2 = n. For n > 3, we define recursively an = an-2 – an-1. Is it true that a2021 is rational? Prove that your answer is correct.
Transcribed Image Text:(a) Prove that n + 2n is divisible by 3 for each n EN. (b) Let z = sin 1 (in radians) and let y = v2. Prove that the following statement is false: (z+ y € Q) A (1- y E Q). (c) Let ai = 1 and let a2 = n. For n > 3, we define recursively an = an-2 – an-1. Is it true that a2021 is rational? Prove that your answer is correct.
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