In an explicit formula, which feature makes the terms of a sequence alternate in sign?

1. A negative base raised to an odd power gives a negative result, and raised to an even power gives a positive result. 2. So a factor of negative one raised to a power involving n flips the sign as n moves from one term to the next. 3. The exponent may be written as n, n + 1 or n - 1, and any of these still produces the alternation. 4. A factorial and a power of positive one are always positive, so neither can change a sign. _Source: OpenStax Algebra and Trigonometry (CC BY 4.0), Ch 13 "Sequences, Probability and Counting Theory", section 13.1 Sequences and Their Notations_