Question

2+4+6+....+160 supra 3+6+9...+240repedeee va rog ofer coroana cine raspunde primul si corect poate castiga ceva

Answer 1

(2+4+6+...+160)/(3+6+9+...+240) =

= 2×(1+2+3+...+80)/3×(1+2+3+...+80) =
(parantezele se reduc)
= 2/3

Answer 2

$\dfrac{2+4+6+...+160}{3+6+9+...+240} = \dfrac{2\cdot (1+2+3+...+80)}{3\cdot (1+2+3+...+80)} = \\\\ \\ = \dfrac{2}{3}\cdot \dfrac{1+2+3+...+80}{1+2+3+...+80} = \dfrac{2}{3}\cdot \left(\dfrac{1+2+3+...+80}{1+2+3+...+80} \right)= \dfrac{2}{3} \cdot 1 = \\ \\\\ = \dfrac{2}{3}$