有關Mathematical Induction

prove by mathematical induction that each of the following is true for all natural numbers n.

1) 1*4 + 2*7 + 3*10... + n(3n+1)= n(n+1)^2

2) 1 + 4 + 4^2... + 4^(n-1) = (1/3) [(4^n)-1]

3) 1*2*3 + 2*3*4 + 3*4*5... + n(n+1)(n+2) = (1/4)n(n+1)(n+2)(n+3)

4) [(1*4)/(2*3)] + [(2*5)/(3*4)] + [(3*6)/(4*5)]... + [n(n+3)]/[(n+1)(n+2)] = [n(n+1)]/(n+2)

5) [(1^2)/(1*3)] + [(2^2)/(3*5)]... + (n^2)/[(2n-1)(2n+1)] = [n(n+1)]/[2(2n+1)]

how to prove?