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1/3+1/15+1/35+1/63+1/99+1/143等于几

1/3+1/15+1/35+1/63+1/99+1/143=5/15+1/15+1/35+1/63+1/99+1/143=6/15+1/35+1/63+1/99+1/143=2/5+1/35+1/63+1/99+1/143=14/35+1/35+1/63+1/99+1/143=15/35+1/63+1/99+1/143=3/7+1/63+1/99+1/143=27/63+1/63+1/99+1/143=28/63+1/99+1/143=4/9+1/99+1/143=44/99+1/99+1/143=45/99+1/143=5/11+1/143=65/143+1/143=66/143=6/13

解:1/3+ 1/15+ 1/35+ 1/63+ 1/99+ 1/143=1/(1*3)+ 1/(3*5)+ 1/(5*7)+ 1/(7*9)+ 1/(9*11) +1/(11*13)=*(1- 1/3+ 1/3- 1/5+ 1/5- 1/7+ 1/7- 1/9+ 1/9- 1/11+1/11- 1/13)=*(1- 1/13)=*(12/13)=6/13

1/3+1/15+1/35+1/63+1/99+1/143=1/2*[2*(1/3+1/15+1/35+1/63+1/99+1/143)]=1/2*[2/3+2/15+2/35+2/63+2/99+2/143]=1/2*[(1-1/3)+(1/3-1/5)+(1/5-1/7)+(1/7-1/9)+(1/9-1/11)+(1/11-1/13)]=1/2*(1-1/13)=6/13

1/3+1/15+1/35+1/63+1/99=[(1-1/3)+(1/3-1/5)+(1/5-1/7)+(1/7-1/9)+(1/9-1/11)]÷(3-1)=[1-1/3+1/3-1/5+1/5-1/7+1/7-1/9+1/9-1/11]÷2=(1-1/11)÷2=5/11裂项分拆:1/(a*b)=(1/a-1/b)÷(b-a)

1/3+1/15+1/35+1/63+1/99+1/143=1/2x(1-1/3)+1/2x(1/3-1/5)+..1/2x(1/9-1/11)+1/2(1/11-1/13)=1/2x(1-1/3+1/3-1/5+.+1/9-1/11+1/11-1/13)=1/2x(1-1/13)=1/2x12/13=6/13

1/3+1/15+1/35+1/63+1/99+1/143=1/1*3+1/3*5+1/5*7+1/7*9+1/9*11+1/11*13=1/2*(1-1/3)+1/2*(1/3-1/5)+1/2*(1/5-1/7)+1/2*(1/7-1/9)+1/2*(1/9-1/11)+1/2*(1/11-1/13)=1/2*(1-1/3+1/3-1/5+1/5-1/7+1/7-1/9+1/9-1/11+1/11-1/13)=1/2*(1-1/13)=1/2*12/13=6/13

1/3+1/15+1/35+1/63+1/99+1/143=1/2x(1-1/3)+1/2x(1/3-1/5)+..1/2x(1/9-1/11)+1/2(1/11-1/13)=1/2x(1-1/3+1/3-1/5+.+1/9-1/11+1/11-1/13)=1/2x(1-1/13)=1/2x12/13=6/13

1/3+1/15=1/3*(1+1/5)=1/3*6/5=2/52/5+1/35=1/5*(2+1/7)=1/5*15/7=3/7自己算下去吧

1/3=1/2*(1/1 -1/3) 1/15=1/2*(1/3 -1/5) 1/35=1/2*(1/5 -1/7) 1/63=1/2*(1/7 -1/9) 1/99=1/2*(1/9 -1/11)6 1/143=1/2*(1/11 -1/13) 所以结果=1/2*(1 -1/13)=6/13

1/3+1/15+1/35+1/63+1/99+1/143=1/2x(1-1/3)+1/2x(1/3-1/5)+..1/2x(1/9-1/11)+1/2(1/11-1/13)=1/2x(1-1/3+1/3-1/5+.+1/9-1/11+1/11-1/13)=1/2x(1-1/13)=1/2x12/13=6/13

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