We cut a cake using n cuts. Each cut is downwards (as you would usually cut a cake), and is a straight line all the way through. Each pair of cuts crosses in exactly one point, and no three cuts cross in the same point. Find a recurrence relation for d(n), the number of pieces of cake created by n cuts. Then, sum the recurrence equations in the following way: d(n) = d(n - 1) = d(2) = + and find an explicit formula for d(n). Start by showing that 1+2+...+n= n(n + 1) 2