Question

what is the formula of the set {-1, 1, -1, 1, ...} without using -1 or exponents

Answer 1

\[\left\{ (-1)^n \right\}_{n=1}^{n}\] That's the way you would normally probably state it. The alternate way it sounds like you're looking for would be...\[\left\{ \cos (\pi n) \right\}_{n=1}^{n}\] If you plug in values for n it is the same as you sequence {-1,1,-1...} of course assuming \[n] \epsilon \mathbb{N}\]