Question

Va rog frumos sa ma ajutati
Am nevoie urgenta de ajutor
DAU COROANA

Answer 1

[tex]A=(-1)^{n^2+n}\cdot 1+1\cdot (-1)^{n^3+2n+3}-(-1)^{n^2+4n-5}=\\ (-1)^{n(n+1)}+(-1)^{n^3+2n+3}-(-1)^{n^2+4n-5}\\ 1) n\ par\\ n(n+1)\ par; (-1)^{n(n+1)}=1\\ n^3+2n+3 \ impar; (-1)^{n^3+2n+3}=-1\\ n^2+4n-5\ impar; (-1)^{n^2+4n-5}=-1\\ A=1-1-(-1)=1-1+1=1\\ 2) n \ impar\\ n(n+1)\ par; (-1); (-1)^{n(n+1)}=1\\ n^3+2n+3\ par; (-1)^{n^3+2n+3}=1\\ n^2+4n-5 \ par; (-1)^{n^2+4n-5}=1\\ A=1+1-1=1\\ deci \ A=1 [/tex]
(∀) $n\in N$