Is There an Alternate Expression for cos(nπ) in Fourier Series?

[erba]

I saw somewhere that an alternate form of cos(n×π) was
cos(n×π) = -1ⁿ⁺¹
But to me this does not make sense. Am I wrong?

For n = 0
cos(n×π) = 1
-1ⁿ⁺¹ = -1

For n = 1
cos(n×π) = -1
-1ⁿ⁺¹ = 1

etc.

Is there another way to express cos(n×π) in an alternate form?

PS. This is related to Fourier series.

 

[erba]

Nevermind, just realized what I did wrong.
I did put -1^n instead of (-1)^n into my calculator.