如果1/2+1/6+1/12+...+1/n(n+1)=2003/2004,那么n的值是多少?
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如果1/2+1/6+1/12+...+1/n(n+1)=2003/2004,那么n的值是多少?
如果1/2+1/6+1/12+...+1/n(n+1)=2003/2004,那么n的值是多少?
如果1/2+1/6+1/12+...+1/n(n+1)=2003/2004,那么n的值是多少?
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))
=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
所以n=2003
1/2+1/6+1/12+...+1/n(n+1)=1-1/2+1/2-1/3+1/3-……+1/n-1/(n+1)
=1-1/(n+1)=n/(n+1)
则 n=2003
1/2+1/6+1/12+...+1/n(n+1)
=1/1*2+1/2*3+……+1/n(n+1)
=1-1/2+1/2-1/3+……+1/n-1/(n+1)
=1-1/(n+1)
=n/(n+1)=2003/2004
所以n=2003