pure maths MI

Q1: For any integer n, let An=[1/(2^n*root5)] *[(1+root5)^n-(1-root5)^n] ;
Bn=1/2 *[(1+root5)^n+(1-root5)^n]. Prove by induction that An,Bn are integers. Deduce that [1/(2^n*root5)] *[(1+root5)^2n-(1-root5)^2n] is even.


Q2: guess and prove a formula for tan^-1 (1/n)-tan^-1(1/n+1).