What is the largest number of regions formed by $6$ planes in space?
I found this equation for the maximum number of regions $R_n$ created by $n$ lines: $$\frac{n^2+n+2}{2}$$
This seems to be very similar to the original question, but I don't know how to use it in a way that is helpful.
Hint: For the first problem, you can think about recursion.
$$f(n) = f(n-1) + n$$