Hello,

Since (-1)^n is multiplied with (-1)^n+1 and has the same basis we can add both
-1^n+n+2 which is -1^2n+2

We know that any even or odd numbers (n could be 2,4,6 or 3,5,7), it will always lead to an even answer. The result is therefore always even. The +2 added afterwards will keep the answer even.
We know that a negative number with an exponent will always lead to a positive answer so -1 becomes 1.
The result is C.

Any one can confirm this?