1/1*2+1/2*3+1/3*4+……+1/2004*2005

1/n*(n+1)=1/n-1/(n+1)

1/1*2+1/2*3+1/3*4+……+1/2004*2005
=1-1/2+1/2-1/3+1/3-1/4+......+1/2004-1/2005
=1-1/2005
=2004/2005.

1/1*2+1/2*3+1/3*4+……+1/2004*2005

=(1-1/2) + (1/2-1/3) + (1/3-1/4) +...+ (1/2003-1/2004) + (1/2004-1/2005)

=1 + (1/2-1/2) + (1/3-1/3) + (1/4-1/4) +...+ (1/2004-1/2004) - 1/2005

=1 - 1/2005

=2004/2005

用程序来做
dim a as integer
a=1
for i=2 to 2005
s=s+1/i*(i-1)
next i
print s
--s就是你要求的值

解：原式=1-1/2+1/2-1/3+1/3-1/4+。。。。。。+1/2004-1/2005
=1-1/2005
=2004/2005

1/1*2+1/2*3+1/3*4+……+1/2004*2005
=(1-1/2)+(1/2-1/3)+(1/3-1/4)+...+(1/2003-1/2004)+(1/2004-1/2005)
（中间正负抵消掉）

=1-1/2005
=2004/2005

分成两个数列来做。方法就是楼上的方法