1. If $n$ is a positive integer, then the value of $\frac{\left(1-(-1)^{n+1}\right)\left(n^{2}-1\right)}{2}$ is ( ).
(A) an even number
(B) zero or an odd number
(C) not necessarily an odd number
(D) definitely zero
$-1 .(B)$  
When $n$ is odd, the expression $=0$; when $n$ is even, the original expression is an odd number.