Question

(2/3)⁰ + (2/3)¹ + (2/3)²

prin factor comun va rog!​

Answer 1

Explicație pas cu pas:

${(\frac{2}{3})}^{0} + {(\frac{2}{3})}^{1} + {(\frac{2}{3})}^{2} = \frac{2}{3}({\frac{2}{3})}^{0 - 1} + {(\frac{2}{3})}^{1 - 1} + {(\frac{2}{3})}^{2 - 1}) = \frac{2}{3}( \frac{3}{2} + 1 + \frac{2}{3}) = \frac{2}{3} \times \frac{9 + 6 + 4}{6} = \frac{2}{3} \times \frac{19}{6} = \frac{19}{9}$

Answer 2

$\it \Big(\dfrac{2}{3}\Big)^0+\Big(\dfrac{2}{3}\Big)^1+\Big(\dfrac{2}{3}\Big)^2=1+\dfrac{2}{3}+\dfrac{2}{3}\cdot\dfrac{2}{3}=1+\dfrac{2}{3}\Big(1+\dfrac{2}{3}\Big)=1+\dfrac{2}{3}\cdot\dfrac{5}{3}=\\ \\ \\ =1+\dfrac{10}{9}=\dfrac{19}{9}$