1/6+1/12+1/20+1/30+.+1/600等于多少?
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1/6+1/12+1/20+1/30+.+1/600等于多少?
还有(1+1/2)×(1+1/4)×(1+1/6)×.×(1+1/2008)×(1-1/3)×(1-1/5)×.×(1-1/2007)
还有(1+1/2)×(1+1/4)×(1+1/6)×.×(1+1/2008)×(1-1/3)×(1-1/5)×.×(1-1/2007)
![1/6+1/12+1/20+1/30+.+1/600等于多少?](/uploads/image/z/17183828-20-8.jpg?t=1%2F6%2B1%2F12%2B1%2F20%2B1%2F30%2B.%2B1%2F600%E7%AD%89%E4%BA%8E%E5%A4%9A%E5%B0%91%3F)
1/6+1/12+1/20+1/30+.+1/600
=(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+.+(1/24-1/25)
=1/2-1/25
=23/50
(1+1/2)×(1+1/4)×(1+1/6)×.×(1+1/2008)×(1-1/3)×(1-1/5)×.×(1-1/2007)
=(1+1/2)×(1-1/3)×(1+1/4)×(1-1/5)×.×(1+1/2006)x(1-1/2007)×(1+1/2008)
=3/2*2/3*5/4*4/5*.2007/2006*2006/2007*(1+1/2008)
=2009/2008
=(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+.+(1/24-1/25)
=1/2-1/25
=23/50
(1+1/2)×(1+1/4)×(1+1/6)×.×(1+1/2008)×(1-1/3)×(1-1/5)×.×(1-1/2007)
=(1+1/2)×(1-1/3)×(1+1/4)×(1-1/5)×.×(1+1/2006)x(1-1/2007)×(1+1/2008)
=3/2*2/3*5/4*4/5*.2007/2006*2006/2007*(1+1/2008)
=2009/2008