1/3+1/6+1/10+1/15+1/21+1/28+1/36+1/45+1/55+1/66

1/3+1/6+1/10+1/15+1/21+1/28+1/36+1/45+1/55+1/66
1/3+1/6+1/10+1/15+1/21+1/28+1/36+1/45+1/55+1/66

1/3+1/6+1/10+1/15+1/21+1/28+1/36+1/45+1/55+1/66
1/3+1/6+1/10+1/15+1/21+1/28+1/36+1/45+1/55+1/66=5/6.
你可以找下规律1/3+1/6=1/2,1/3+1/6+1/10=3/5=1.5/2.5,1/3+1/6+1/10+1/15=2/3,1/3+1/6+1/10+1/15+1/21=5/7=2.5/3.5,1/3+1/6+1/10+1/15+1/21+1/28=3/4,规律为每多加一项,值的分子和分母同时+上0.5.
另解,原式=1/3=(1/2-1/3)+(1/6-1/15)+1/15+(1/12-1/28)+1/28+(1/20-1/45)+1/45+(1/30-1/66)+1/66
=1/2+1/6+1/12+1/20+1/30
= 1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6

1/6=1/2-1/3
1/10=1/3*(1/2-1/5)=1/6-1/15
1/21=1/4(1/3-1/7)=1/12-1/28
1/28=1/3(1/4-1/7)=1/12-1/21
1/45=1/12(1/3-1/15)=1/36-1/180
1/55=1/6(1/5-1/11)=1/30-1/66
所以原式=1/2+1/3=5/6