induction proof??

[kai89]

I'm not sure if I'm in the right place but I need help doing this proof.

n! + 2 is divisible by 2, for all integers n is less than or equal to 2.

I'm not sure where to start because of the factorial?
i would appreciate any help i could get thanks

[HallsofIvy]

Since you say "induction proof" you START just the way you always do with induction- prove the base case!

"n! + 2 is divisible by 2, for all integers n is less than or equal to 2."
is surely NOT the problem you want to do! n! is only defined for NONNEGATIVE integers and the only nonnegative integers "less than or equal to 2" are 0, 1 and 2. You don't need induction for that!
I assume you mean "all integers n GREATER than or equal to 2".

Okay, the "base case" is n= 2. 2!= 2 and 2!+ 2= 4 which is surely divisible by 2.

Are you really required to use induction? if n is greater than or equal to 2, then n!= 2(3)(4)...(n) is itself divisible by 2. n!+ 2= 2(3)(4)...(n)+ 2= 2(3(4)...(n)+ 1).