We were asked to prove that for any integer n $\displaystyle sum of C(n,2r) for r >= 0 is equal to sum of C(n,2r-1) for r>= 1 $ where C(n,r) is choosing r objects from n objects.
We were asked to prove that for any integer n sum of C(n,2r) for r >= 0 is equal to sum of C(n,2r-1) for r>= 1 where C(n,r) is choosing r objects from n objects.
Write down the binomial expansion of $\displaystyle (1-1)^n$ (which is equal to 0, of course).