App: Look at the derivative and integral of (x+1)^n

Entree: You might need the identity binom(m,m) + binom(m+1,m)+...+binom(m+p,m)=binom(m+p+1,m+1)

Dessert:  Let p_k,m(x) be the quotient
(x^(k+m)-1)(x^(k+m-1)-1)...(x^(k+1)-1)/[(x^m-1)(x^(m-1)-1)...(x-1)]

and prove that

lim_x-> 1 p_(k,m)(x)=binom(k+m,m).  Now induct on k+m after developing a pascal's triangle for the polynomials