Ignoring the +/- for the moment, when n=1, the term equals 23 , and as n increases by 1, both the numerator and denominator increase by 1. So the fraction is clearly [math]\frac{n+1}{n+2}[\math]
The first, third, fifth, etc term is negative, and the others positive. So when n is odd, it is negative, and when it is even it is positive. You can get that with (−1)n since when n is even, the negatives “cancel out” and when it is odd you end up with -1.
So the nth term will be (−1)n(n+1n+2) .
