(1-1/1006^2)(1-1/1007^2)(1-1/1008^2)……(1-1/2011^2)怎么做?
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(1-1/1006^2)(1-1/1007^2)(1-1/1008^2)……(1-1/2011^2)怎么做?
=(1-1/1006)(1+1/1006)(1-1/1007)(1+1/1007)(1-1/1008)(1+1/1008)……(1-1/2011)(1+1/2011)
=1005/1006 × 1007/1006×1006/1007 × 1008/1007×1007/1008 × …… ×2011/2010×2010/2011 ×2012/2011
=1005/1006 ×2012/2011
=2010/2011
等于2010/2011
=(1-1/1006)(1+1/1006)(1-1/1007)(1+1/1007)(1-1/1008)(1+1/1008)……(1-1/2011)(1+1/2011)
=1005/1006 × 1007/1006×1006/1007 × 1008/1007×1007/1008 × …… ×2011/2010×2010/2011 ×2012/2011
=1005/1006 ×201...
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=(1-1/1006)(1+1/1006)(1-1/1007)(1+1/1007)(1-1/1008)(1+1/1008)……(1-1/2011)(1+1/2011)
=1005/1006 × 1007/1006×1006/1007 × 1008/1007×1007/1008 × …… ×2011/2010×2010/2011 ×2012/2011
=1005/1006 ×2012/2011
=2010/2011
收起
1/2+2/3+3/4+..1005*1/1006
2012*(1-1/2+1/4-1/503+1/1006-1/2012)最好能简便
计算(√2+1)^2012*(3-2√2)^1006
(1-1/1006^2)(1-1/1007^2)(1-1/1008^2)……(1-1/2011^2)怎么做?
[1+2+3+4+5+...+2009+2010]/[(1-1/1006)(1-1/1007)...(1-1/2009)(1-1/2010)]
[1+2+3+4+5+...+2009+2010]/[(1-1/1006)(1-1/1007)...(1-1/2009)(1-1/2010)]
(2010-1)+(2009-2)+(2008-3)+.+(1006-1005)=
1+2+3+4+5+...+2005+2006/(1-1/1004)(1-1/1005)(1-1/1006)(1-1/2007)...(1-1/2005)(1-1/2006)
1-2+3-4+5……=2009-2010+2111=?是-1006吗嗯嗯,是打错了.是2011 是-1006,还是1006?
(2+1)(2²+1)(2的四次方+1)……(2的1006次方+1)+1
简便计算,(1-1/2+1/3-1/4+1/5-…+1/2007-1/2008)/(1/1005+1/1006+1/1007+…1/2007+1/2008)
(1-1/2+1/3-1/4+1/5-…+1/2007-1/2008)除以(1/1005+1/1006+…1/2007+1/2008)=?急
(1/1004-1)*(1/1005-1)*(1/1006-1).(1/2004-1)=?
计算:(1/2008-1)(1/2007-1)...(1/1006-1)(1/1005-1)帮忙下哈
(1-1/2+1/3-1/4.+1/2007-1/2008)÷(1/1005+1/1006+1/1007+.1/2008)今天是最后一天,
(1-1/2+1/3-1/4...+1/2007-1/2008)÷(1/1005+1/1006+1/1007+...+1/2008)等于多少?
计算:(1-1/2+1/3-1/4+...+1/2007-1/2008)/(1/1005+1/1006+1/1007+...+1/2008)
(1-1/2+1/3-1/4+...+1/2007-1/2008)/(1/1005+1/1006+1/1007+...+1/2008)=0的计算公式