Unit 15 Exercises
1. Find f(1), f(2), and f(3), if f(n) is defined recursively by f(0) = 2 and for n = 0, 1, 2, ...
a) f(n + 1) = f(n) + 2.
b) f(n + 1) = 3f(n).
c) f(n + 1) = 2f(n).
2. Find f(2), f(3), and f(4), if f(n) is defined recursively by f(0) = 1, f(1) = -2 and for n= 1, 2,...
a) f(n + 1) = f(n) + 3f(n - 1).
b) f(n + 1) = f(n)2 f(n - 1).
3. Let F be the function such that F(n) is the sum of the first n positive integers. Give a recursive definition of F(n).
4. Give a recursive algorithm for computing nx whenever n is a positive interger and x is an integer.
5. Give a recursive algorithm for finding the sum of the first n odd positive integers.