Question

Calculati:6•(1+2+3+.....+100)²:[3•(1+2+3+..+100)]:(1+2+3+....+100)

Answer 1

6·(1+2+3+.........+100)²:[3·(1+2+3+.......+100)]:(1+2+3+........+100)= 6·[100·(100+1):2]²:{3·[100·(100+1):2}:[100·(100+1):2]=
6·(50·101)²:[3·(50·101]:(50·101)=
6·5050²:3·5050:5050=
6·25502500:15150:5050=
153015000:15150:5050=
10100:5050=2

Answer 2

Regula lui gauss spune: S=$\frac{n(n+1)}{2}$
Relatia devine: 6*($\frac{100*101}{2}$)²:3($\frac{100*101}{2}$:$\frac{100*101}{2}$)
=6*(5050)²:(3*5050):5050
=6*5050²:3
=2*5050²