Ummm somehow my question was removed.

(a) Show that (p+q)(p^n+q^n) - pq(p^(n-1)+q^(n-1)) = p^(n+1) + q^(n+1) for n is greater than or equal to 1.

(b) Given S = a^n + b^n and the roots of the equation x^2 + 2x + 5 = 0, what is S when n=1,2,3,4...10.

Could someone please show me how to prove these questions?

For (a), I have found how to prove LHS = RHS but I cannot prove that this only applies when n is greater than or equal to 1.

For (b), do I simply use the quadratic formula to find a and b, and then substitute it with the value of n into S = a^n + b^n to find S?