1/1*3+1/3*5+1/5*7+.1/17*19+1/19*21怎么简便计算?

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1/1*3+1/3*5+1/5*7+.1/17*19+1/19*21怎么简便计算?
1/1*3+1/3*5+1/5*7+.1/17*19+1/19*21怎么简便计算?

1/1*3+1/3*5+1/5*7+.1/17*19+1/19*21怎么简便计算?
1/1*3+1/3*5+1/5*7+.1/17*19+1/19*21
=【（1-1-3）+（1/3-1/5）+（1/5-1/7）……+（1/17-1/19）+（1/19-1/21）】÷2
=【1-1-3+1/3-1/5+1/5-1/7……+1/17-1/19+1/19-1/21】÷2
=【1-1/21】÷2
=20/21÷2
=10/21
很高兴为你解答,

分数裂项
1/(1×3)=(1-1/3)÷2
1/(3×5)=(1/3-1/5)÷2
......
1/(19×21)=(1/19-1/21)÷2
原式=(1-1/3+1/3-1/5+...+1/19-1/21)÷2
=(1-1/21)÷2
=20/21÷2
=10/21

1/1*3+1/3*5+1/5*7+....1/17*19+1/19*21
=1/2(1/1-1/3+1/3-1/5+……+1/17-1/19+1/19-1/21)
=1/2(1-1/21)
=1/2*20/21
=10/21

1/1*3+1/3*5+1/5*7+....1/17*19+1/19*21
=(1/2)*(1-1/3+1/3-1/5+1/5-1/7+....+1/17-1/19+1/19-1/21)
=(1/2)*(1-1/21)
=(1/2)*(20/21)
=10/21
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1-3+5-7+... (1+1/3+1/5+1/7)*(1/3+1/5+1/7+1/9)-(1+1/3+1/5+1/7+1/9)*(1/3+1/5+1/7) 简算(1+1/3+1/5+1/7)*(1/3+1/5+1/7+1/9)-(1+1/3+1/5+1/7+1/9)*(1/3+1/5+1/7) 简便计算 1/1*3+1/1*3*5+1/1*3*5*7+1/1*3*5*7*9-73/945 1/3+1/5+1/7+.+1/2n+1 (1/3+1/5+1/7)*(1/5+1/7+1/9)-(1/3+1/5+1/7+1/9)*(1/5+1/7)=? 1 1 1 1 1 3 5 7 1 5 13 25 1 7 25 why 1/1×3+1/3×5+1/5×7+1/7×9.+1/2011×2013 简算:1/1*3+1/3*5+1/5*7+1/7*9+1/9*11 1/1*3+1/3*5+1/5*7+1/7*9+...1/17*19= 计算1/(1×3)+1/(3×5)+1/(5×7)+1/(7×9)+.+1/(19×21) 1/1×3+1/3×5+1/5×7+1/7×9+.+1/2013×2015 1/1*3+1/3*5+1/5*7+1/7*9+.+1/101*103 帮帮忙1/1*3+1/3*5+1/5*7+1/7*9+...1/99*101 1/1*3+1/3*5+1/5*7+1/7*9+1/49*51= 计算：1/1×3+1/3×5+1/5×7+1/7×9``````+1/2001×2003 (1*3)/1+(3*5)/1+(5*7)/1+(7*9)/1+(9*11)/1 1/1*3+1/3*5+1/5*7+1/7*9+1/9*11 (1*3)/1+(3*5)/1+(5*7)/1+(7*9)/1+(9*11)/1