1/1*2*3+1/2*3*4+……+1/n(n+1)(n+2)
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1/n(n+1)(n+2)
=1/n(n+2)-1/(n+1)(n+2)=(1/2)[1/n-1/(n+2)]-[1/(n+1)-1/(n+2)]
左边=(1/2)*(1/1*2-1/2*3)+(1/2)(1/2*3-1/3*4)+……+(1/2)[1/n(n+1)-1/(n+1)(n+2)]
=(1/2)*(1/1*2-1/2*3+1/2*3-1/3*4+……+1/n(n+1)-1/(n+1)(n+2)]
=(1/2)*(1/1*2-1/(n+1)(n+2)]
=1/4-1/2(n+1)(n+2)<1/4
=1/n(n+2)-1/(n+1)(n+2)=(1/2)[1/n-1/(n+2)]-[1/(n+1)-1/(n+2)]
左边=(1/2)*(1/1*2-1/2*3)+(1/2)(1/2*3-1/3*4)+……+(1/2)[1/n(n+1)-1/(n+1)(n+2)]
=(1/2)*(1/1*2-1/2*3+1/2*3-1/3*4+……+1/n(n+1)-1/(n+1)(n+2)]
=(1/2)*(1/1*2-1/(n+1)(n+2)]
=1/4-1/2(n+1)(n+2)<1/4
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