1/[n×(n+1)]=1/n-1/(n+1)
∴原式=(1/3-1/4)+(1/4-1/5)+(1/5-1/6)+(1/6-1/7)+(1/7-1/8)+(1/8-1/9)
=1/3-1/9
=2/9
1/3x4+1/4x5+1/5x6+1/6x7+1/7x8+1/8x9
=1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7+1/7-1/8+1/8-1/9
=1/3-1/9
=2/9
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