1/13+1/24+1/35+……+1/911

来源：百度知道编辑：UC知道时间：2024/05/14 00:56:29

1/1*3+1/2*4+1/3*5+……+1/9*11 给出过程及化简的内容！
谢谢咯!

1/n(n+2)=1/2*(1/n-1/(n+2))
所以1/1*3+1/2*4+1/3*5+……+1/9*11=1/2*[1-1/3+1/2-1/4+1/3-1/5+...+1/9-1/11]=1/2*(1+1/2-1/10-1/11)=1/2*144/110=36/55

1/1*3+1/2*4+1/3*5+……+1/9*11
=0.5(1-1/3+1/2-1/4+1/3-1/5+...+1/9-1/11)
=0.5(1+1/2-1/10-1/11)
=36/55

=(1/1*3+1/3*5+……+1/9*11)+(1/2*4+……+1/8*10)
=(1/2)*(1-1/3+1/3-1/5+……+1/9-1/11)+(1/2)*(1/2-1/4+1/4-1/6+1/6-1/8+1/8-1/10)
=(1/2)(1-1/11)+1/2*(1/2-1/10)
=36/55

(1/2005-1)(1/2004-1)........(1/3-1)(1/2-1) (1-1/100)(1-1/99)(1-1/98)......(1-1/3 1+1/2+1/3+.....+1/n 1+1/2+1/3+...+1/100 1+1/3+1/6+........+1/55 1-1/2+1/3-.....-1/10 (1+1/2+1/3+1/4)× (1-1/2)(1-1/3)(1-1/4)(1-1/5).....(1-1/1000) 3,1/3,1/3,1/,1/27,1/27( ) 1+1/2+1+1/3+1+1/4+......+1/100=?