In any sequence of ~$n$~ nonzero numbers, a pair of consecutive terms with opposite signs represents a sign change. For example, the sequence -2, 3,-4, 5 has three sign changes. Does the sequence of nonzero numbers ~$s_1,s_2,\ldots, s_n$~ have an even number of sign changes?
1. ~$s_k = (-1)^k$~ for all positive integers ~$k$~ from 1 to ~$n$~.
2. ~$n$~ is odd.