if x/a + y/b =1 and( x^2)/a + ( y^2)/b =(ab/(a+b)) then prove for all n belongs to N
x^(n+1)/a + y^(n+1)/b = (ab/(a+b))^n
There is a clue in what is given; they constitute not a single base case to start from, but force the truth of what is to be proven for the n=0 and n=1 cases. This implies that you are probably going to have to use something like strong induction (or at least the assumed truth of cases k and k-1 to prove it for k+1) to do this.
CB