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1/3+13/15+33/35+61/63+97/99的简便方法
人气:218 ℃ 时间:2020-05-20 15:10:06
解答
1/3 +13/15 +33/35 +61/63 +97/99
=(3-2)/3 +(15-2)/15 +(35-2)/35 +(63-2)/63 +(99-2)/99
=5 -(2/3+2/15+2/35+2/63+2/99)
=5-[2/(1×3)+2/(3×5)+2/(5×7)+2/(7×9)+2/(9×11)]
=5-(1-1/3+1/3-1/5+1/5-1/7+1/7-1/9+1/9-1/11)
=5-(1-1/11)
=5-10/11
=45/11
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