Pascal Identity is: C(n,k)= C(n-1, k-1) + C(n-1, k)

C(m+n, m+1) = C(m+n-1, m) + C(m+n-1, m+1)

= C(m+n-1, m) + C(m+n-2, m)+C(m+n-2, m+1)

= C(m+n-1, m) + C(m+n-2, m)+C(m+n-3, m)+C(m+n-3, m+1)

= ..........

= C(m+n-1, m) + C(m+n-2, m)+....+C(m, m)+C(m, m+1)

= C(m+n-1, m) + C(m+n-2, m)+....+C(m, m)

Note: C(m, m+1) = 0 because you cannot get m+1 apples from m apples.