几道数学题,高分悬赏

1.1/2*5+1/5*8+1/8*11+…+1/1994*1997
=1/3*[(1/2-1/5)+(1/5-1/8)+...+(1/1994-1/1997)]
=1/3*(1/2-1/1997)
=165/3994
2.1/(1*2*3)+1/(2*3*4)+1/(3*4*5)+……+1/(97*98*99)+1/(98*99*100)
=[1/(1*2)-1/(2*3)+1/(2*3)-1/(3*4)+.....+1/(97*98)-1/(98*99)+1/(98*99)
-1/(99*100)]/2
=[1/2-1/9900]/2
=4949/19800
3.1＋3 1/6+5 1/12+7 1/20+9 1/30+11 1/42+13 1/56+15 1/72+17 1/90
=1+3+5+7+9+11+13+15+17+(1/6+1/121/20+1/30+1/42+1/56+1/72+1/90)
=18*4+9+1/2-1/3+1/3-1/4+……+1/9-1/10=1/2-1/10
=81+2/5
=407/5
(1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90=
1/6=1/2-1/3
1/12=1/3-1/4
........
1/90=1/9-1/10
所以相加为1/2-1/3+1/3-1/4+……+1/9-1/10=1/2-1/10=2/5 )
4.1－5/6+7/12-9/20+11/30-13/42+15/56-17/72.
=1/6 + 7/12 - 9/20 + 11/30 - 13/42 + 15/56 - 17/72
=3/4 - 9/20 + 11/30 - 13/40 + 15/56 - 17/72
=3/10 + 11/30 - 13/42 + 15/56 - 17/72
=2/3 - 13/42 + 15/56 - 17/72
=5/14 + 15/56 - 17/72
=