B.
B.
Induction step: Assume the theorem is true for k. Show that it holds for k+1.
In order to get the exponents in the two summations the same, substitute i+1 = j in the right summation (this will also change the bounds of the summation). This yields
The indexes don't go over the same bounds. Thus I'll move the first summation's first term out of the summation and I'll move the second summation's last term out of the summation. For consistency I'll use index variable j in both summations. This yields
Applying Pascal's rule we get