Recursive Function Example

Fredrick Eisele

The recursive function is $$ f(n)= \begin{cases} 0, & \text{if $x \le 0$}.\\\\ f(n-1) + n, & \text{otherwise}. \end{cases} $$ Assume \( f \) is of the form \( \frac{n(n+1)}{2} \); then $$ f(0) = \frac{0(0+1)}{2} = 0 $$ $$ f(n) = \frac{n(n+1)}{2} = f(n-1) + n = \frac{[n-1]([n-1]+1)}{2} + n $$

Keith E. Peterson

This is only true of recursive functions that work on numbers.

Fredrick Eisele

Sorry, what?

Are you commenting on the content or the format?

Keith E. Peterson

Just the content. lol