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.

 

Answers for these exercises