1/3+1/5+1/7+1/9+1/11+1/33+1/35+1/45+1/55+1/77=?

洋气蛋 1年前他留下的回答 已收到1个回答

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该名网友总共回答了16个问题，此问答他的回答如下：采纳率：93.8%

1/3+1/5+1/7+1/9+1/11+1/33+1/35+1/45+1/55+1/77
=1/3+1/5+1/7+1/9+1/11+(1/3-1/11)/8+(1/5-1/7)/2
+(1/5-1/9)/4+(1/5-1/11)/6+(1/7-1/11)/4
=1/3+1/5+1/7+1/9+1/11+(1/3)/8-(1/11)/8+(1/5)/2-(1/7)/2+
(1/5)/4-(1/9)/4+(1/5)/6-(1/11)/6+(1/7)/4-(1/11)/4
=(1/3)*[1+1/8]
+(1/5)*[1+1/2+1/4+1/6]
+(1/7)*[1-1/2+1/4]
+(1/11)*[1-1/8-1/6-1/4]
+(1/9)*[1-1/4]
=(1/3)*(9/8)+(1/5)*(23/12)+(1/7)*(3/4)+(1/11)*(11/24)+(1/9)*(3/4)
=(1/3)*(9/8)+(1/5)*(23/12)+(1/7)*(3/4)+1/24+1/12
=(3/8)+(1/5)*(23/12)+(1/7)*(3/4)+1/8
=1/2+(1/5)*(23/12)+(1/7)*(3/4)
=(6*5*7+23*7+3*3*5)/(12*5*7)
=[210+161+45]/(12*5*7)
=416/(12*5*7)
=104/105

1年前他留下的回答

6

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