Problem Solving

If n is a postive interger, which of the following must be an even interger?

n+1
n+2
n^2+2
n^2+n
n^2+2n

answer is n^2+n

take any two consecutive integers , they differ by one hence one is odd and the other is even .If you multiply the two you always get an even number

if n is an integer then n and n+1 are consecutive integers
when you multiply n and n+1 you should get an even number

n*(n+1) = even ------------n^2+n is even