Induction · Superchallenge problem

Planes in general position: when the $(k + 1)$-th plane is added, the $k$ old planes cut it along $k$ lines in general position, which divide it into $R(k) = 1 + \dfrac{k(k + 1)}{2}$ pieces, and each piece splits a region of space in two. How many regions do $10$ planes make?