Question

Calculati:
1-2+2^2-2^3+..........+2^8=

Answer 1

[tex] 1-2+2^2-2^3+...+2^8 =? \\ \\ $Avem de a face cu o progresie geometrica.\\ \\ \left\| \begin{array}{c} b_1 = 1 \\ q = -2 \\ n = 9 \end{array} \right| \Rightarrow S_9 = b_1\cdot \dfrac{q^{9}-1}{q-1} = 1\cdot \dfrac{(-2)^9-1}{-2-1} =\dfrac{-2^9-1}{-3} = \dfrac{2^9+1}{3} \\ \\ \\ \Rightarrow \boxed{1-2+2^2-2^3+...+2^8 = \dfrac{2^9+1}{3}}[/tex]