Question

简算：2/3×5+2/5×7+2/7×9+2/9×11+1/11

Answer 1

2/3×5+2/5×7+2/7×9+2/9×11+1/11
=(5-3)/(3×5)+(7-5)/(5×7)+(9-7)/(7×9)+(11-9)/(9×11)+1/11
=1/3-1/5+1/5-1/7+1/7-1/9+1/9-1/11+1/11
=1/3

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追问

1/3-1/5+1/5-1/7+1/7-1/9+1/9-1/11+1/11这一步什么意思

追答

(5-3)/(3×5)=5/15-3/15=1/3-1/5
(7-5)/(5×7)=7/35-5/35=1/5-1/7
。。。。。

所以
(5-3)/(3×5)+(7-5)/(5×7)+(9-7)/(7×9)+(11-9)/(9×11)+1/11
=1/3-1/5+1/5-1/7+1/7-1/9+1/9-1/11+1/11