Most regions cut out by ten lines

Ten straight lines are drawn in the plane, no two of them parallel. What is the largest number of separate regions the plane can be split into? (As a check, one line gives $2$ regions.)

$56$. The $k$-th line can cross the previous $k-1$ lines in at most $k-1$ points, so it cuts through at most $k$ existing regions and adds $k$ new ones; general position achieves this. Hence $L_n=1+\tfrac{n(n+1)}{2}$, and $L_{10}=56$.