496,473 views
37 votes
37 votes
Find a closed-form formula that reproduces the sequence 1,-1, 1, -1, 1, -1, 1, ... (zero-based indexing). Check all that are correct.

User Saccarab
by
2.5k points

1 Answer

11 votes
11 votes

Recall that


\cos(0) = \cos(2\pi) = \cos(4\pi) = \cos(2n\pi) = 1

and


\cos(\pi) = \cos(3\pi) = \cos(5\pi) = \cos((2n+1)\pi) = -1

Then the given sequence could be written as


a_n = \cos(n\pi) = (-1)^n

User Alexfv
by
2.8k points