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.](/uploads/image/z/15257025-9-5.jpg?t=%E5%B7%B2%E7%9F%A51%2F2%2B1%2F6%2B1%2F12%2B%E2%80%A6%E2%80%A6%2B1%2Fn%EF%BC%88n%2B1%29%3D2003%2F2004%2C%E6%B1%82n%E7%9A%84%E5%80%BC.)
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