Question

Cele doua subpuncte c) si d) va rog . Ofer coroana . Multumesc !

Answer 1

[tex]a)\frac{3}{4}\cdot(-1)^3-(-\frac{3}{5})^{-1}+\frac{(-1)^{2009}}{2}=\\ \\ -\frac{3}{4}+\frac{5}{3}-\frac{1}{2}=\frac{-9+20-6}{12}=\boxed{\frac{5}{12}}\\ \\ b)\frac{1}{3}\cdot(-1)^n+\frac{1}{2}\cdot(-1)^{n+1}+\frac{1}{6}\cdot (-1)^{n+2}=\\ Aici\ distingem\ doua\ cazuri\ posibile:\\ 1)n-impar (n=2k+1)\\ 2)n-par(n=2k)\\ Pentru\ primul\ caz:\\ \frac{1}{3}\cdot(-1)^{2k+1}+\frac{1}{2}\cdot(-1)^{2k+2}+\frac{1}{6}\cdot(-1)^{2k+3}=\\ \\ -\frac{1}{3}+\frac{1}{2}-\frac{1}{6}=\boxed{0}\\ [/tex]
[tex]Pentru\ al\ doilea\ caz:\\ \frac{1}{3}\cdot(-1)^{2k}+\frac{1}{2}\cdot(-1)^{2k+1}+\frac{1}{6}\cdot(-1)^{2k+2}=\\ \\ \frac{1}{3}-\frac{1}{2}+\frac{1}{6}=\boxed{0}\\ Se\ pare\ ca\ in\ ambele\ cazuri\ da\ 0. :))[/tex]