1. a) Suppose that f is defined recursively by: f (0) = 5 and f(n+1) = 2 fn+ 5. Find f( 1), (2), (3) and f(4)? b) For which positive integer n is it true that 2">n³? c) Prove your answer in (b) above using mathematical induction. d) Give a recursive definition of the sequence {an}, n= 1, 2, 3... if an = 2" + 1
1. a) Suppose that f is defined recursively by: f (0) = 5 and f(n+1) = 2 fn+ 5. Find f( 1), (2), (3) and f(4)? b) For which positive integer n is it true that 2">n³? c) Prove your answer in (b) above using mathematical induction. d) Give a recursive definition of the sequence {an}, n= 1, 2, 3... if an = 2" + 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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