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