1. Write a formula for the function f: N→ Z defined by the recursive formula f(n) = nf(n-1) +1 n-1 when the base of the recursion is (i) f(1) = 1; (ii) f(1) = 2; (iii) f(1) = -1.
1. Write a formula for the function f: N→ Z defined by the recursive formula f(n) = nf(n-1) +1 n-1 when the base of the recursion is (i) f(1) = 1; (ii) f(1) = 2; (iii) f(1) = -1.
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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![1. Write a formula for the function f: N→ Z defined by the recursive formula
nf(n-1) +1
f(n)
n-1
when the base of the recursion is
(i) f(1) = 1;
(ii) f(1) = 2;
(iii) f(1) = -1.
2. Identify the sets X CZ defined by the following recursive definitions.
(a) 0 € X, 1 € X, x, y ≤X →x · y € X.
(b) 0 € X, 1 X, x, y ≤X →x+y € X.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F05500500-114e-4276-a5a0-70319270c08c%2F2cdcfb3b-375c-41df-9b1d-ead006d90da3%2Fnvas0o_processed.jpeg&w=3840&q=75)
Transcribed Image Text:1. Write a formula for the function f: N→ Z defined by the recursive formula
nf(n-1) +1
f(n)
n-1
when the base of the recursion is
(i) f(1) = 1;
(ii) f(1) = 2;
(iii) f(1) = -1.
2. Identify the sets X CZ defined by the following recursive definitions.
(a) 0 € X, 1 € X, x, y ≤X →x · y € X.
(b) 0 € X, 1 X, x, y ≤X →x+y € X.
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