1/23+1/34+1/45+……+1/20012002

来源：百度知道编辑：UC知道时间：2024/06/23 09:08:37

1/(2*3)=1/2-1/3
1/(3*4)=1/3-1/4
1/2-1/3+1/3-1/4+1/4-1/5+......1/2000-1/2001+1/2001-1/2002
=1/2-1/2002
=500/1001

1/2-1/3+1/3-1/4。。。。。-1/2001+1/2001-1/2002=1/2-1/2002=2001/4004

1/2*3+1/3*4+1/4*5+……+1/2001*2002

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

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

=1/2-1/2002

=500/1001

1/2*3=1/2-1/3(=1/6);
1/3*4=1/3-1/4(=1/12);
1/4*5=1/4-1/5(=1/20);
... ...
1/2001*2002=1/2001-1/2002;
则有
1/2*3+1/3*4+1/4*5+……+1/2001*2002=1/2-1/3+1/3-1/4+1/4-1/5+... ...+1/2001-1/2002;
化简得 1/2-1/2002=1001/2002-1/2002=1000/2002=500/1001

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)× 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) (1/2005-1)(1/2004-1)........(1/3-1)(1/2-1) 1+1/2+1/3+.....+1/2005][1/2+1/3+.......+1/2006]-[1/2+1/3+......+1/2005][1+1/2+1/3+1/2006] (1-1/2-1/3-...-1/2001)*(1/2+1/3+...1/2002)-(1-1/2-1/3-...1/2002)*(1/2+1/3+...+1/2001) 1/1+1/2+1/3+1/4+。。。。+1/N 是多少