3分之1加15分之1加35分之1加63分之1加99分之1等于多少

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3分之1加15分之1加35分之1加63分之1加99分之1等于多少

3分之1加15分之1加35分之1加63分之1加99分之1等于多少
3分之1加15分之1加35分之1加63分之1加99分之1等于多少

3分之1加15分之1加35分之1加63分之1加99分之1等于多少
3分之1加15分之1加35分之1加63分之1加99分之1
=1/(1x3)+1/(3x5)+1/(5x7)+1/(7x9)+1/(9x11)
=1/2(1-1/3+1/3-1/5+1/5-1/7+1/7-1/9+1/9-1/11)
=1/2x(1-1/11)
=1/2x10/11
=5/11

11分之5

11分之5.按从前往后的循序通分相加再约分即可。

1/3+1/15+1/35+1/63+1/99
=1/3+1/(3×5)+1/(5×7)+1/(7×9)+1/(9×11)
=5/(3×5)+1/(3×5)+9/(5×7×9)+5/(5×7×9)+1/(9×11)
=6/(3×5)+14/(5×7×9)+1/(9×11)
=2/5+2/(5×9)+1/(9×11)
=2/5+(2×11)/(5×9×11)+...

全部展开

1/3+1/15+1/35+1/63+1/99
=1/3+1/(3×5)+1/(5×7)+1/(7×9)+1/(9×11)
=5/(3×5)+1/(3×5)+9/(5×7×9)+5/(5×7×9)+1/(9×11)
=6/(3×5)+14/(5×7×9)+1/(9×11)
=2/5+2/(5×9)+1/(9×11)
=2/5+(2×11)/(5×9×11)+(1×5)/(5×9×11)
=2/5+27/(5×9×11)
=2/5+3/(5×11)
=(2×11)/(5×11)+3/(5×11)
=25/(5×11)
=5/11

收起

11分之5