Question

1/(1*2*3)+1/(2*3*4)+1/(3*4*5)+...+1/(9*10*11)简便运算

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Answer 1

1/(1*2*3)+1/(2*3*4)+1/(3*4*5)+...+1/(9*10*11)
=1/2[1/(1×2)-1/(2×3)+1/(2×3)-1/(3×4)+...+1/(9×10)-1/(10×11)]
=1/2×[1/(1×2)-1/(10×11)]
=1/2×(1/2-1/110)
=1/2×54/110
=27/110
公式:1/n(n+1)(n+2)=1/2[1/n(n+1)-1/(n+1)(n+2)]
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