Mathematic induction

Let P(n) be the statement: n(n^2 - 1) is divisible by 6

When n = 1

1(1^2 - 1) = 0 which is divisible by 6

So, P(1) is true

Assume that P(k) is true. i.e. k(k^2 - 1) is divisible by 6

when n = k + 1

(k + 1)[(k + 1 )^2 - 1]

= (k + 1)(k^2 + 2k)

= k(k + 1)(k + 2)

= (k - 1)k(k + 1) + 3k(k + 1)

= 6M + 3k(k + 1) (by the assumption of P(k))

= 6M + 6N (As there should be a even number among k and k + 1)

= 6(M + N) which is divisible by 6

So, P(k + 1) is true

By mathematial induction, for all natural number n, P(n) is true.

^_^

When I finished typing, I was already too late.

Please read:
http://postimg.org/image/yrgf9hkad/

In this way, you can use MI completely.

2013-10-07 00:47:38 補充：
客氣了～　myisland8132 也答得很好～ ^_^