已知1/2+1/6+1/12+……+1/n(n+1)=2003/2004,求n的值.
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已知1/2+1/6+1/12+……+1/n(n+1)=2003/2004,求n的值.
已知1/2+1/6+1/12+……+1/n(n+1)=2003/2004,求n的值.
已知1/2+1/6+1/12+……+1/n(n+1)=2003/2004,求n的值.
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)
∵1/2+1/6+1/12+……+1/n(n+1)=2003/2004
∴n/(n+1)=2003/2004
n=2003
1/2+1/6+1/12+……+1/n(n+1)
=1/1-1/2+1/2-1/3+......+1/n-1/(n+1)
=1-1/(1+n)
=n/(n+1)
=2003/2004
n=2003
N=2003