Use the principle of mathematical induction to prove (in Description below)

Question

Use the principle of mathematical induction to prove:

For any integer n ≥ 1,

Answer 1

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

= n/(n+1) + 1/((n+1)(n+2)) =

(n(n+2) + 1) / ((n+1)(n+2)) =

(n^2 + 2n + 1)/ ((n+1)(n+2)) =

(n+1)^2 / ((n+1)(n+2)) =

(n+1)/(n+2)