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
\[ f(0) = \frac{0(0+1)}{2} = 0 \]
\[ f(n) = \frac{n(n+1)}{2} = f(n-1) + n = \frac{[n-1]([n-1]+1)}{2} + n \]