我的青春小鸟不回来:1/(1*2)+1/(2*3)+1/(3*4)+1/(4*5 )+...+1/(2000*2001)+1/(2001*2002)=

来源：百度文库 编辑：高考问答 时间：2024/07/04 20:07:32

1/2*3=1/2-1/3,1/3*4=1/3-1/4,...,
原式=1/1-1/2+1/2-1/3+1/3-1/4+...+1/2000-1/2001+1/2001-1/2002
=1-1/2002=2001/2002

2001/2002

原式=1-1/2+1/2-1/3……-1/2001+1/2001-1/2002=2001/2002

1/(1*2)+1/(2*3)+1/(3*4)+1/(4*5 )+...+1/(2000*2001)+1/(2001*2002)
=1-1/2+1/2-1/3+1/3-1/4+……+1/2001-1/2002
=1-1/2002
=2001/2002

1+1/1+2/=?? 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+......+10 (1-1/2^2)(1-1/3^2)....(1-1/10^2) (1-1/2^2)(1-1/3^2)....(1-1/10^2) 3/2=2+1/1*2=1/1+1/2 (1/2005-1)(1/2004-1)........(1/3-1)(1/2-1) 1/1+1/2+1/3+1/4+。。。。+1/N 是多少 《1/2》专辑 1/2超柔线损