1-1/2+1/6+1/12+1/20+·········+1/72+1/90巧算

1-1/2+1/6+1/12+1/20+·········+1/72+1/90巧算
1-1/2+1/6+1/12+1/20+·········+1/72+1/90巧算

1-1/2+1/6+1/12+1/20+·········+1/72+1/90巧算
1-1/2+1/2*3+1/3*4+1/4*5……+1/8*9+1/9*10
=1-1/2+1/2-1/3+1/4-1/4+1/4-1/6+……+1/8-1/9+1/9-1/10
=1-1/10
=9/10

规律：每项=1/n(n+1)=1/n-1/(n+1)
原式=1-1/2+1/2-1/3+1/3-1/4+......+1/9-1/10=9/10