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](/uploads/image/z/590955-51-5.jpg?t=1%2F6%2B1%2F12%2B1%2F20%2B1%2F30%2B1%2F42%2B1%2F56%2B%2B1%2F72%2B1%2F81%2B1%2F90)
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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