1/6+1/12+1/20+1/30+1/42+1/56++1/72+1/81+1/90

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1/6+1/12+1/20+1/30+1/42+1/56++1/72+1/81+1/90
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1/6+1/12+1/20+1/30+1/42+1/56++1/72+1/81+1/90
1/6+1/12+1/20+1/30+1/42+1/56++1/72+1/81+1/90

1/6+1/12+1/20+1/30+1/42+1/56++1/72+1/81+1/90
=1/(2+3)+1/(3+4)+1/(4+5).
=1/2-1/3+1/3-1/4+...+1/9-1/10
=1/2-1/10
=2/5

(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+(1/5-1/6)+(1/6-1/7)+(1/7-1/8)+(1/8-1/9)+1/81+(1/9-1/10)=1/2+1/81-1/10剩下的自己算

405分之167

求分母的最小公倍数，同分求和呗

原式=1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7+1/7-1/8+1/8-1/9+1/9-1/10
=1/2-1/10
=2/5