1-1/1+2-1/1+2+3-1/1+2+3+4…-1/1+2+3…+100

1/1*2=1 - 1/2 1/2*3=1/2 - 1/3,1/3*4=1/3 - 1/4利用这个规律计算1/1*2+.

=(1-1/2)+(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+……+(1/98-1/99)+(1/99-1/100)=1-1/100=99/100

(1 - 1/2)*(1 - 1/3)*(1 - 1/4)..*(1 - 1/100) 用简便方法计算

用平方差原式=(1-1/2)(1+1/2)(1-1/3)(1+1/3)(1-1/4)(1+1/4)……(1-1/100)(1+1/100)=(1/2)(3/2)(2/3)(4/3)(3/4)(5/4)……(99/100)(101/100)中间约分=(1/2)(101/100)=101/200

[1 - 1/(2^2)][1 - 1/(3^2)][1 - 1/(4^2)]……[1 - 1/(100^2)]用简便方法

[1-1/(2^2)][1-1/(3^2)][1-1/(4^2)]……[1-1/(100^2)] =(1-1/2)(1+1/2)(1-1/3)(1+1/3)..(1-1/100)(1+1/100) =1/2*3/2*2/3*4/3*..*99/100*101/100 =1/2*101/100 =101/200

1/1 - 1/2 2/2 - 1/2 1/3 - 2/3 3/3 - 2/3 1/3 1/4以此类推 第2012个数是多少

1/2

1/1, - 1/2,2/2 , - 1/2,1/3, - 2/3,3/3, - 2/3,1/3, - 1/4,2/4 - 3/4,..那么7/11是这.

是第107个

一道数学题.|1 - 1\2|+|1\2 - 1\3|+|1\3 - 1\4|+|1\5 - 1\6|+|1\7 - 1\8|+|1\9.

|1-1\2|+|1\2-1\3|+|1\3-1\4|+|1\5-1\6|+|1\7-1\8|+|1\9-1\10|…|1\99-1\100| =(1-1/2)+(1/2-1/3)+……+(1/99-1/100) =1-1/100 =99/100

(1+1/2)*(1 - 1/2)*(1+1/3)*(1 - 1/3)*..*(1+1/99)*

将加的相乘 再乘以 减的相乘(1+1/2)(1+1/3)(1+1/4)……(1+1/100)*(1-1/2)(1-1/3)(1-1/4)……(1-1/100)=3/2*4/3*5/4……101/100*1/2*2/3*3/4*……*99/100=101/2*1/100=101/200 求采纳为满意回答.

1/1+(2/1 - 1/2)+(3/1 - 2/2+1/3)+(4/1 - 3/2+2/3 - 1/4)+.+(9/1 - 8/2+.

1/1+(2/1-1/2)+(3/1-2/2+1/3)+(4/1-3/2+2/3-1/4)+…+(9/1-8/2+7/3-6/4+…+1/9)=(1/1+2/1+3/1+4/1…+9/1)+(-1/2-2/2-3/2…-8/2)+(1/3+2/3…7/3)+…+(1/9)=45+36/2+28/3+21/4+15/5+10/6+6/7+3/8+1/9=45+18+28/3+21/4+3+5/3+6/7+3/8+1/9=66+11+45/8+6/7+1/9=77+45/8+6/7+1/9行了 自己通分吧

- 1*1/2 - 1/2*1/3 - 1/3*1/4 … - 1/2015*1/2016=

如果 -1*2=-1+2,-1/2*1/3=-1/2+1/3,-1/3*1/4=-1/3+1/4……那么 (-1*2)+(-1/2*1/3)+(-1/3*1/4)……(-1/2016*1/2017)=(-1+2)+(-1/2+1/3)+(-1/3+1/4)……(-1/2016+1/2017)=-1+2-1/2+1/2017=1/2+1/2017=2019/4034问题已解决记的采纳,点击 右下的 采纳.

(1 - 1/2)+(1/2 - 1/3)+(1/3 - 1/4)+……+(1/2014 - 1/2015)+(1/2015 - 1/2.

1-1/2+1/2-1/3+1/3-1/4+1/4+..-1/2015+1/2015-1/2016=1-1/2016=2015/2016