Question

rezultatul calculului (-1)^5^1+(-1)^5^2+(-1)^5^3+... + (-1)^5^2014

Answer 1

$S=(-1)^{5^{1}}+(-1)^{5^{2}} +(-1)^{5^{3}}+...+(-1)^{5^{2014}}. \\ \\ 5^1,~5^2,~5^3,...,5^{2014}~sunt~numere~impare,~deci~ (-1)^{5^{n}}=-1. \\ \\ Prin~urmare: \\ \\ S=(-1)+(-1)+(-1)+...+(-1)= \\ ~~~=(-1) \cdot 2014= \\ ~~~= \boxed{-2014}.$

$Precizare:~n \in \{1,2,3,...,2014\}.$