Hi could some do this question for me I have never derived a recurrence before
For an integer $n \geq 1$, draw $n$ straight lines, such that no two of them are parallel and no three of them intersect in one single point. These lines divide the plane into regions (some of which are bounded and some of which are unbounded). Denote the number of these regions by $R_n$.
Derive a recurrence for the numbers $R_n$ and use it to prove that for $n \geq 1$,
$$ R_n = 1 + n(n+1)/2 $$