三级训练数学题12分之1加20分之1加30分之1加42分之1加56分之1加72分之1等于多少?

1/12+1/20+1/30+1/42+1/56+1/72
=1/3*4+1/4*5+1/5*6+1/6*7+1/7*8+1/8*9
=(1/3-1/4)+(1/4-1/5)+(1/5-1/6)+(1/6-1/7)+(1/7-1/8)+(1/8-1/9)
=1/3-1/9
=2/9

原式=1/3*4+1/4*5+....+1/8*9
=1/3-1/4+1/4-1/5+...+1/8-1/9
=1/3-1/9
=2/9

2/9

1/12=1/3-1/4
1/20=1/4-1/5
1/30=1/5-1/6
1/42=1/6-1/7
1/56=1/7-1/8
1/72=1/8-1/9
上面六个式子相加，右边刚好剩下1/3-1/9
1/12+1/20+1/30+1/42+1/56+1/72＝1/3-1/9＝2/9

12分之1加20分之1加30分之1加42分之1加56分之1加72分之1
=1/3*4+1/4*5+.+1/8*9
=1/3-1/4+1/4-1/5+...+1/8-1/9
=1/3-1/9
=2/9

原式=1/(3*4)+1/(4*5)+^^^^^+1/(8*9)
=1/3-1/4+1/4-1/5+……+1/8-1/9
=1/3-1/9
=2/9