kill(all)$

van=facebook.com/LearningCalculus$

f(a,b,n):=(a+b)^n;

g(a,b,n):=sum(a^(n-k)*b^k,k,0,n);

        for n:0 thru 5 do
            if n#0 then
            (
                print("     :", [a,b,n], "   f: ", expand(f(a,b,n))),
                print("                  g: ", g(a,b,n)),
                print("                f-g: ", fullratsimp(f(a,b,n)-g(a,b,n))));