Into how many chunks can one cut a round piece of cheese with n straight cuts?
Consider the $3D$ version
My try:
f(x) = number of pieces and $'x'$ as number of cuts.
$f(1)=2$
$f(2)= 2 + f(1)$
and therefore
$f(n) = n + f(n-1) $ and after solving the recurrence relation I got
$f(n) = [n^{2}+n+2]/2 $
Is this correct?