# Recursion

Determine whether each of these proposed definitions is a valid recursive definition of a function f from the set of non negative integers to the set of integers. If f is well

defined, find a formula for f(n) when n is a non negative integer and prove that your formula is valid.

a) f(0) = 1,f(n) = - f(n - 1) for n >= 1

b) f(0) = 1, f(1) = 0, f(2) = 2, f(n) = 2f(n - 3) for n>=3

c) f(0) = 0, f(1) = 1, f(n) = 2f(n + 1) for n >= 2

d) f(0) = 0, f(1) = 1, f(n) = 2f(n - 1) for n >= 1

e) f(0) = 2, f(n) = fen - 1) if n is odd and n >= 1 and f(n) = 2f(n - 2) if n >= 2

https://brainmass.com/math/discrete-structures/recursion-recursive-functions-353219

#### Solution Preview

Determine whether each of these proposed definitions is a valid recursive definition of a function f from the set of non negative integers to the set of integers. If f is well

defined, find a formula for f(n) when n is a non negative integer and prove that your formula is valid.

a) f(0) = 1,f(n) = - f(n - 1) for n >= 1

b) f(0) = 1, f(1) = 0, f(2) = 2, f(n) = 2f(n - 3) for n>=3

c) f(0) = 0, f(1) = 1, f(n) = 2f(n + 1) for n >= 2

d) f(0) = 0, ...

#### Solution Summary

Recursion is demonstrated for proposed functions.