Hi, I've got a question which asks if n(n+1) is even for all n>0.
I'm just wondering if "even" just means divisible by 2.
so I got on my paper
Showing that statement is true for n=1:
1(2)=2 which is divisible by 2
Assuming that statement is true for n=k:
k(k+1)=
=2a where a is an interger.
Proving that statement is true for n=k+1:
(k+1)(k+2)=![](https://latex.codecogs.com/png.latex?\bg_white k^2+3k+2)
=2a +2k+2
=2(a+k+1)
which is divisible by 2 as a+k+1 is an interger.
[Then the mouthful about if statement is tru for n=k, it is also.... blah]
This is correct, right?
I'm just wondering if "even" just means divisible by 2.
so I got on my paper
Showing that statement is true for n=1:
1(2)=2 which is divisible by 2
Assuming that statement is true for n=k:
k(k+1)=
Proving that statement is true for n=k+1:
(k+1)(k+2)=
=2a +2k+2
=2(a+k+1)
which is divisible by 2 as a+k+1 is an interger.
[Then the mouthful about if statement is tru for n=k, it is also.... blah]
This is correct, right?