1/20+1/30+1/42+1/56+1/72+1/90=

=(1/4-1/5)+(1/5-1/6)+(1/6-1/7)+(1/7-1/8)+(1/8-1/9)+(1/9-1/10)
=1/4-1/10
=0.15

1/20=1/4-1/5=(5-4)/(4*5)=1/20
1/30=1/5-1/6
1/42=1/6-1/7
1/56=1/7-1/8
1/72=1/8-1/9
1/90=1/9-1/10
两边相加，左边为所求式，
右边=1/4-1/10=10/40-4/40=6/40=3/20

1/20+1/30+1/42+1/56+1/72+1/90
=1/(4*5)+1/(5*6)+1/(6*7)+1/(7*8)+1/(8*9)+1/(9*10)
=1/4-1/5+1/5-1/6+...+1/9-1/10
=1/4-1/10
=3/20.

1/20+1/30+1/42+1/56+1/72+1/90
=1/4*5+1/5*6+1/6*7+1/7*8+1/8*9+1/9*10
=(1/4-1/5)+(1/5-1/6)+……+(1/9-1/10)
=1/4-1/10
=3/20

=1/（4*5）+1/（5*6）+1/（6*7）+1/（7*8）+1/（8*9）+1/（9*10）
=1/4-1/5+1/5-1/6+1/6-1/7+1/7-1/8+1/8-1/9+1/9-1/10
=1/4-1/20
=3/20

1/20+1/30+1/42+1/56+1/72+1/90
=1/(4*5)+1/(5*6)+1/(6*7)+1/(7*8)+1/(8*9)+1/(9*10)
=1/4-1/5+1/5-1/6+...+1/9-1/10
=1/4-1/10
=3/20.应该这样做