3分之1+15分之1+35分之1+63分之1+99分之1+143分之1 简便运算怎么做?
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1/3 + 1/15 + 1/35 + 1/63 + 1/99 + 1/143
= 1/3 + 1/3 x 1/5 + 1/5 x 1/7 + 1/7 x 1/9 + 1/9 x 1/11 + 1/11 x 1/13
= 1/3 (1 + 1/5) + 1/7 (1/5 + 1/9) + 1/11 (1/9 + 1/13)
=1/3 x 6/5 + 1/7 x 14/45 + 1/11 x 22/117
=2/5 + 2/45 + 2/117 (注:2/5 + 2/45 = 18/45 + 2/45 = 20/45 = 4/9)
=4/9 + 2/117 (注:4/9 + 2/117 = 54 /117 + 2/117 = 54/117(同时除以9)=6/13 )
=6/13
= 1/3 + 1/3 x 1/5 + 1/5 x 1/7 + 1/7 x 1/9 + 1/9 x 1/11 + 1/11 x 1/13
= 1/3 (1 + 1/5) + 1/7 (1/5 + 1/9) + 1/11 (1/9 + 1/13)
=1/3 x 6/5 + 1/7 x 14/45 + 1/11 x 22/117
=2/5 + 2/45 + 2/117 (注:2/5 + 2/45 = 18/45 + 2/45 = 20/45 = 4/9)
=4/9 + 2/117 (注:4/9 + 2/117 = 54 /117 + 2/117 = 54/117(同时除以9)=6/13 )
=6/13
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