如果1/2+1/6+1/12+.+1/n(n+1)=2003/2004 ,n=

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如果1/2+1/6+1/12+.+1/n(n+1)=2003/2004 ,n=
如果1/2+1/6+1/12+.+1/n(n+1)=2003/2004 ,n=

如果1/2+1/6+1/12+.+1/n(n+1)=2003/2004 ,n=
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

1/2+1/6+1/12+。。。。+1/n(n+1)=2003/2004
1-1/2+1/2-1/3+1/3-1/4+...+1/n-1/(n+1)=2003/2004
1-1/(n+1)=2003/2004
n/(n+1)=2003/2004
n=2003

1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+....-1/n+1
=1-1/n+1
=n/n+1
故n=2003