1/2+1/6+1/12+1/20.+1/(n-1)n=

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1/2+1/6+1/12+1/20.+1/(n-1)n=1/2+1/6+1/12+1/20.+1/(n-1)n=1/2+1/6+1/12+1/20.+1/(n-1)n=由于1/(n-1)n=1/(n-

1/2+1/6+1/12+1/20.+1/(n-1)n=
1/2+1/6+1/12+1/20.+1/(n-1)n=

1/2+1/6+1/12+1/20.+1/(n-1)n=
由于1/(n-1)n=1/(n-1)-1/n
所以1/2+1/6+1/12+1/20.+1/(n-1)n=(1-1/2)+(1/2-1/3)+(1/3-1/4)+.+(1/(n-1)-1/n)=1-1/2+1/2-1/3+1/3-1/4+.+1/(n-1)-1/n=1-1/n

(n-1)/n


1/2+1/6+1/12+1/20.......+1/(n-1)n
=1/2+(1/2-1/3)+(1/3)-1/4)+....(1/(n-1)-1/n)
=1-1/n
=(n-1)/n