How many series of length $n$ over the group {+1,-1} follow: $$a_1a_2a_3...a_n=-1$$ I know that there must be a odd number of -1 terms in the product, I noticed the pattern of $2^{n-1}$ and tried to prove it by using induction but got stuck. Any hint will help.
2026-04-05 17:47:44.1775411264
combinatorics; possibilities of product
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