For how many integers where 2 <= n <= 100 is n(n + 1) odd?
Let's see if we can detect a trend
n n + 1 Product
2 3 6
3 4 12
4 5 20
5 6 30
6 7 42
I don't think we have to go any further to see what's always going to happen.
This illustrates that no matter what n equals, then either n or n+1 will always be even.
The product of an even number and any other number is always even.
The answer to the problem is NONE of them will be odd.