Question

1/2+1/6+1/12+1/20+1/30+1/42= 2+4+6+...+2010= (5/9-5/6+1/4)÷(-1/36)= (-19 18/19)*38= 都用简便计算

Answer 1

1/2+1/6+1/12+1/20+1/30+1/42=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7=1-1/7=6/7
2+4+6+...+2010=2*(1+2+3+...+1005)=2*1005*1006/2=1011030
(5/9-5/6+1/4)÷(-1/36)= -36*(5/9-5/6+1/4)= -20+30-9=1
抱歉最后一个你题目少写了运算符号了吧，请追问，谢谢

Answer 2

1/2+1/6+1/12+1/20+1/30+1/42=1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7=6/7
2+4+6+...+2010=2*{[(1+1005)*1005]/2}=1005*1006=(1000+5)*1006=1006000+5030=1011030
(5/9-5/6+1/4)÷(-1/36)=(5/9-5/6+1/4)*(-36)=-(20-30+9)=1
(-19 18/19)*38=-(19*38+18/19*38)=-（19²*2+18*2）=-[（20-1）²*2+36]
=-[（400-40+1）*2+36]=-(361*2+36)=-(722+36)=-758