35. Prove the combinatorial identity



n − 1 i − 1



=



n i



−

 n i + 1



+···± 

n n



, i  n

(a) by induction on i

(b) by a backwards induction argument on i—that is, prove it first for i = n, then assume it for i = k and show that this implies that it is true for i = k − 1.