1/(n-1）×n×（n+1)=[1/(n-1）×n-1/n×（n+1）]/2
所以原式=（1/1x2-1/2x3)/2+(1/2x3-1/3x4)/2+(1/3x4-1/4x5)/2+……+(1/9x10-1/10x11)/2
=(1/1x2 -1/2x3+1/2x3 -1/3x4+1/3x4 -1/4x5+……+1/9x10-1/10x11)/2
=(1/1x2-1/10x11)/2
=27/110
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