1-1/2=1/2,1/2-1/3=1/6=1/2*3,1/3-1/4=1/12=1/3*4,1/4-1/5=1/20=1/4*5.再计算下列各式的值(1) 1/1*2+1/2*3+1/3*4+1/4*5+.1/99*100(2)1/3+1/15+1/35+1/63+.1/17*19

(1)1-1/2-1/6-1/12-1/20-.....-1/9900
=1-1/2-(1/2-1/3)-(1/3-1/4)-(1/4-1/5)-……-(1/99-1/100)
=1-1/2-1/2+1/3-1/3+1/4-1/4+1/5-……-1/99+1/100
=1-1/2-1/2+1/100
=1/100

1/1*2+1/2*3+1/3*4+1/4*5+......1/99*100
=1/2+1/6+1/12+1/20+......1/9900
=(1-1/2)+(/2-1/3)+(1/3-1/4)+(1/4-1/5)+......(1/99-1/100)
=1-1/2+/2-1/3+1/3-1/4+1/4-1/5+......1/99-1/100
=1-1/100
=99/100
1/3+1/15+1/35+1/63+......1/17*19
=1/2*(2/3+2/15+2/35+2/63+......2/17*19 )
=1/2*{(1-1/3)+(1/3-1/5)+(1/3-1/5)+......(1/17-1/19)
=1/2*(1-1/3+1/3-1/5+1/3-1/5+......1/17-1/19)
=1/2*(1-1/19)
=1/2*18/19
=9/19

1）原式=1-1/2+1/2-1/3+1/3+......+1/99-1/100
=1-1/100
=99/100
2)原式=1/1*3+1/3*5+1/5*7+......+1/17*19
=2*(1-1/3+1/3-1/5+1/5-1/7......+1/17-1/19)
=2*18/19
=36/19

（1）=1-1/2+1/2-1/3+1/3-1/4.....+1/99-1/100=1-1/100=99/100
（2）=（1/2）*（1-1/3+1/3-1/5+1/5-1/7......+1/17-1/19）
=（1/2）*（1-1/19）=9/19

(1)原式等于(1-1/2)+（1/2-1/3）+（1/3-1/4）+（1/4-1/5）+……+（1/99-1/100）【去括号】=1-1/100=99/100
（2）原式等于1/（1*3）+1/（3*5）+1/（5*7）+1/（7*9）+……+1/（17*19）=1-1/3+1/3-1/5+1/5-1/7+1/7-1/9+……+1/17-1/19=1-1/19=18/19

（1）原式=（1-1/2)+(1/2-1/3)...+(1/99-1/100)=1-1/100=99/100
前一个括号内的第二项与后一个括号内的第一项，一正一负抵去
（2）原式=1/1*3+1/3*5+...+1/17*19=1/2[(1-1/3)+(1/3-1/5)+...+(1/17-1/19)]=1/2(1-1/19)=9/19