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问题: 数学

1*2*3的倒数加2*3*4的倒数加3*4*5的倒数...

解答:

1/(1*2*3)+1/(2*3*4)+1/(3*4*5)+.............+1/n(n+1)(n+2)=
(1/2)*{[1/(1*2)-1/(2*3)]+[(1/(2*3)-1/(3*4)]+[(1/(3*4)-1/(4*5)]+.............+(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)]