Question

Fractia (1+2+3+…+24)/(3+6+9+…+45) este?

Answer 1

$\displaystyle \frac{1+2+3+...+24}{3+6+9+...+45} =\frac{1+2+3+...+24}{3(1+2+3+...+15)} =\frac{\cfrac{24(24+1)}{2} }{3 \cdot \cfrac{15(15+1)}{2} } =\\\\=\frac{\cfrac{24 \cdot 25}{2} }{\cfrac{3 \cdot 15 \cdot 16}{2} } =\frac{\cfrac{600}{2} }{\cfrac{720}{2} }=\frac{600}{\not2} \cdot \frac{\not2}{720} =\frac{600}{720}=\frac{5}{6}$