1/12+1/23+1/34+1/45+...+1/2001*2002 =?

来源：百度知道编辑：UC知道时间：2024/06/27 21:41:40

1/1*2+1/2*3+1/3*4+1/4*5+...+1/2001*2002 =?

给你个很像的题
http://zhidao.baidu.com/question/27433719.html

1/1*2+1/2*3+1/3*4+1/4*5+……+1/2001*2002
=(1-1/2)+(1/2-1/3)+(1/3-1/4)+(1/4-1/5+……+ (1/2001-1/2002)
=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+……-1/2001 + 1/2001-1/2002
=1-1/2002
=2001/2002

拆项法

1/1*2+1/2*3+1/3*4+1/4*5+...+1/2001*2002
=1/2+1/2-1/3+1/3-1/4+1/4-1/5+......-1/2001+1/2001-1/2002
=1-1/2002
=2001/2002

2001/2002

1+1/(1+2)+1/(1+2+3)+...+1/(1+2+3+...+100) 1+1/(1+2)+1/(1+2+3)+-------+1/(1+2+3+----+100) 1+1/1+2+1/1+2+3+...+1/1+2+3...+2000 1*(1/1+2)*(1/1+2+3)*~~~*(1/1+2+~~~2005)=? 1+1/2+1/3+.....+1/n 1+1/2+1/3+...+1/100 1-1/2+1/3-.....-1/10 (1+1/2+1/3+1/4)× 3/2=2+1/1*2=1/1+1/2 (1/2005-1)(1/2004-1)........(1/3-1)(1/2-1)