1—1／2+1／6+1／12+1／20+.+1／72+1／90

1—1／2+1／6+1／12+1／20+.+1／72+1／90
1—1／2+1／6+1／12+1／20+.+1／72+1／90

1—1／2+1／6+1／12+1／20+.+1／72+1／90
原式=1-1/2+1/2*3+1/3*4+……+1/9*10
=(1-1/2)+(1/2-1/3)+(1/3-1/4)+……+(1/9-1/10)
=1-1/10
=9/10

1—1／2+1／6+1／12+1／20+......+1／72+1／90
=1-1+1/2+1/2-1/3+1/3-1/4+...+1/9-1/10
=1-1/10
=9/10

1—1／2+1／6+1／12+1／20+......+1／72+1／90
=1-1/2+1/2-1/3+1/3-1/4+....+1/9-1/10
=1-1/10
=9/10

原式=
1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90
=1/(1*2)+1/(2*3)+1/(3*4)+1/(4*5)+1/(5*6)+1/(6*7)+1/(7*8)+1/(8*9)+1/(9*10)
=1-1/2+(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+(1/5-1/6)+(1/6-1/7)+(1/7-1/8)+(1/8-1/9)+(1/9-1/10)
=1-1/10 （打开括号）
=9/10
注：1/n(n+1) =1/n-1/(n+1)