Question

Calculati:
b)[(2+4+...+700)*189]:[(4+8+...+360)*39]
c) (6+12+258):(3+6+...+129)

Answer 1

b)[(2+4+...+700)*189]:[(4+8+...+360)*39]=
=[2(1+2+...+350)*189]:[4(1+2+...+90)*39]=
=[(2*350*351/2)*189]:[(4*90*91/2)*39]=
=(350*351*189):(2*90*91*39)=
=(350*351*189):(180*91*39)=
=(35*9*189):(18*91)=
=(35*189):(2*91)=
=(35*27):(2*13)=
=945/26

c) (6+12+...+258):(3+6+...+129) =
=6(1+2+...+43):3(1+2+...+43) =
=2