Question

se considera numerele a=1+2+3+.....+48 si b=1+2+3+....+63
determinati raportul numerelor a si b

Answer 1

Folosim suma lui Gauss in ambele numere:
$a = \frac{48*49}{2}$
$b = \frac{63*64}{2}$

Atunci raportul numerelor a si b este:
$\frac{a}{b}=\frac{\frac{48*49}{2}}{\frac{63*64}{2}} = \frac{48*49}{2} * \frac{2}{63*64} = \frac{48*49}{63*64} = \frac{6*7}{9*8}=\ \textgreater \ \frac{a}{b}=\frac{3*7}{9*4} =\ \textgreater \ \\ =\ \textgreater \ \frac{a}{b}=\frac{1*7}{3*4} =\ \textgreater \ \frac{a}{b}=\frac{7}{12}$