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For a natural number n, we define n! = 1-2-3 (n − 1). n. - For example: 2! = 1-2, 3! = 1-2-3 = 6, 5!= 1-2-3-4-5 = 120. (a) Compute 6! and 7!. (In each case, simplify and express your final answer as a single integer.) (b) Prove that if n, mEN, and n > m, then n! > m!. (c) Let x E R. Prove that for all n € N, if x ≥n, then x" ≥n!. .

For a natural number n, we define n! = 1-2-3 (n − 1). n. - For example: 2! = 1-2, 3! = 1-2-3 = 6, 5!= 1-2-3-4-5 = 120. (a) Compute 6! and 7!. (In each case, simplify and express your final answer as a single integer.) (b) Prove that if n, mEN, and n > m, then n! > m!. (c) Let x E R. Prove that for all n € N, if x ≥n, then x" ≥n!. .

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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For a natural number n, we define n! = 1-2-3 (n − 1). n. For example: 2! = 1-2, 3!= 1-2-3=6,5!= 1-2-3-4-5 = 120. (a) Compute 6! and 7!. (In each case, simplify and express your final answer as a single integer.) (b) Prove that if n, mN, and n > m, then n! > m!. (c) Let x E R. Prove that for all n € N, if x ≥n, then x ≥n!. .
Transcribed Image Text:For a natural number n, we define n! = 1-2-3 (n − 1). n. For example: 2! = 1-2, 3!= 1-2-3=6,5!= 1-2-3-4-5 = 120. (a) Compute 6! and 7!. (In each case, simplify and express your final answer as a single integer.) (b) Prove that if n, mN, and n > m, then n! > m!. (c) Let x E R. Prove that for all n € N, if x ≥n, then x ≥n!. .
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