(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?
(1-1/1006^2)(1-1/1007^2)(1-1/1008^2)……(1-1/2011^2)怎么做?

(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