Question

Calculati (1+2+3.......+2743)/2743
[(2+4+...+700)*189/[4+8+....360)*39]
(6+12+....+258)/3+6+....+129)

Answer 1

1.
(1+2+3.......+2743)/2743= 2743*2744:2 / 2743= 2744 : 2=1372


2.
[(2+4+...+700)*189] /[4+8+....360)*39]= 189*702*350/2 / 39*364*90/2=

= 189*702*175 / 39*364*45= 3³*7*2*3³*13*5²*7 : 3*13* 2²*7*13 *3²*5 =

=3³*7*5* :  2*13 =945/26
 
3.
(6+12+....+258)/ (3+6+....+129)=6*(1+2+...+43) / 3*(1+2+3+...43)=

=6//3=2 (se reduc parantezele)