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

Name: ANSWER ANY FOUR (4) QUESTIONS FROM THIS SECTION1. a)Suppose that fis
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Description: ANSWER ANY FOUR (4) QUESTIONS FROM THIS SECTION1. a)Suppose that fis defined recursively by:f (0) = 5 and f(n+1) = 2 fn+ 5. Find f(1), (2), (3) and (4)?b)For which positive integer n is it true that 2">n3?c)Prove your answer in (b) above using mathe

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. а) Suppose that fis defined recursively by: f (0) = 5 and f(n+1) = 2 fn +5. Find A1), A2), (3) and f4)? 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 e) Use your definition in (d) above to find a10, and a15 f) Let A = {1, 2, {{1,2}}}. Find the power set P(A)
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Why [0,1] is the set of all subsequential limits? Could you explain in detail?