如果1/2+1/6+1/12+.+1/n(n+1)=2003/2004 ,n=
问题描述：
如果1/2+1/6+1/12+.+1/n(n+1)=2003/2004 ,n=
答
1/2+1/6+1/12+...+1/[n(n+1)]
=1/(1×2)+1/(2×3)+1/(3×4)+...+1/[n(n+1)]
=1-1/2+1/2-1/3+1/3-1/4+...+1/n-1/(n+1)
=1-1/(n+1)
=n/(n+1)
=2003/2004
n=2003