Did you mean (-1)^2? Since that's just 1, I wonder if you meant something else. Maybe (-1)^(2+2n), but that's also just 1. Anyway, a monotone increasing sequence is just one with the property that each term is greater than or equal to the previous term. A strict monotone increasing sequence has every term strictly greater than the previous. And monotone decreasing sequences are defined exactly how you'd think.