Give a recursive definition with initial condition(s). The initial conditions can start at any appropriate number (i.e., you don’t necessarily need to start at 1).Please help with questions 4-9 1. The function f(n) = 2", n = 1, 2, 3, ...2. The function f(n) = n!, n = 0, 1, 2,...3. The function f(n) = 5n + 2, n = 1, 2, 3, ...4. The sequence ai == 16, a2 = 13, az = 10, as = 7, ...5. The Fibonacci numbers 1, 1, 2, 3, 5, 8, 13, ...6. The set S, = {0,3, 6,9,...,3n}, n= 0,1,2, ...7. The set S, = {1,5,9, 13, 17,..., 1+ 4n}, n = 0, 1, 2,...%3D8. The set S, = {1,1/3,1/9,1/27,..., 1/3"}, n = 0, 1, 2, ...9. The set S, ={-2n,..., -4, -2,0, 2, 4, 6,..., 2n}, n = 0,1,2,...

The recursive definition is used to define a sequence. The initial condition can be used to obtain…

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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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Give a recursive definition with initial condition(s). The initial conditions can start at any appropriate number (i.e., you don’t necessarily need to start at 1).

Please help with questions 4-9

1. The function f(n) = 2", n = 1, 2, 3, ...
2. The function f(n) = n!, n = 0, 1, 2,...
3. The function f(n) = 5n + 2, n = 1, 2, 3, ...
4. The sequence ai =
= 16, a2 = 13, az = 10, as = 7, ...
5. The Fibonacci numbers 1, 1, 2, 3, 5, 8, 13, ...
6. The set S, = {0,3, 6,9,...,3n}, n= 0,1,2, ...
7. The set S, = {1,5,9, 13, 17,..., 1+ 4n}, n = 0, 1, 2,...
%3D
8. The set S, = {1,1/3,1/9,1/27,..., 1/3"}, n = 0, 1, 2, ...
9. The set S, ={-2n,..., -4, -2,0, 2, 4, 6,..., 2n}, n = 0,1,2,...

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