1/1*2*3=0.5/1-1/2+0.5/3
1/2*3*4=0.5/2-1/3+0.5/4
............
1/n(n+1)(n+2)=0.5/n-1/(n+1)+0.5/(n+2)
以上所有式子相加，错项相加减得：
1/1*2*3+1/2*3*4+...+1/n(n+1)(n+2)=0.5/1-0.5/2-0.5/(n+1)+0.5/(n+2)=1/4-0.5/[(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)]
=1/4-2/(4n²+12n+8)
=(n²+3n)/(4n²+12n+8)
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