Question

When you cut a pizza, you cut along a diameter of the pizza. let p(n) be the number of slices of pizza that exist after you have made n cuts, where n ≥ 1. write a recurrence for p(n).?

Answer 1

Each cut will double the number of slices, so if the recurrence starts with
`n=1`, then you have
`p(n)=2^(n-1)`.


`p(1)=2^(1-1)=2^0=1` corresponds to the whole pizza (one "slice").

The first cut gives
`p(2)=2^(2-1)=2^1=2` slices, and so on.