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

1/1*2+1/2*3+1/3*4+1/4*5+1/5*6+1/6*7=1/2(1+1/3)+1/4(1/3+1/5)+1/6(1/5+1/7)=2/3+2/15+2/35=6/7
首先这是个等差数列，公差为2首项为2 ，2010为第n项，则2+（n-1）*2=2010，计算的n=1005， 则2+4+6+……+2010=1005*（2+2010）/2=1011030
后面的式子看不懂

Answer 2

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)
=1-1/2+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× [ (1+1004)×1004÷2 +1005 ]
=2× [ 1005×502+1005 ]
=2×1005×503
=2010×503
= 1011030

(5/9-5/6+1/4)÷(-1/36)
=(5/9)×(-36)-(5/6)×(-36)+(1/4)×(-36)
=-20+30-9
=10-9
=1

(-19 18/19)*38
=-1918×38÷19
=-1918×2
=-3836