Dividing a Pizza with N Lines

Question

How many regions can we divide a pizza with n lines?

I can not find a formula.

Lines Pieces
0 1
1 2
2 4

Answer 1

You're looking for the Lazy Caterer's Sequence as given in: https://oeis.org/A000124

The formula is $\frac{n(n+1)}{2} + 1$, where $n$ starts from $0$.

A simple proof can be found here in this Wikipedia article: https://en.wikipedia.org/wiki/Lazy_caterer%27s_sequence

Answer 2

Lazy caterer's sequence formula:

$p=\frac{n^{2} + n + 2}{2}$