计算:(1-1/2²)(1-1/3²)(1-1/4²)……(1-1/2010²)
来源:学生作业帮 编辑:作业帮 分类:数学作业 时间:2024/08/24 07:47:04
计算:(1-1/2²)(1-1/3²)(1-1/4²)……(1-1/2010²)(1-1/2011²)
(1-1/2²)(1-1/3²)(1-1/4²)……(1-1/2010²)(1-1/2011²)
=(1-1/2)(1+1/2)(1-1/3)(1+1/3)(1-1/4)(1+1/4)*.(1-1/2010)(1+1/2010)(1-1/2011)(1+1/2011)
=1/2*3/2*2/3*4/3*3/4*5/4*.2009/2010*2011/2010*2010/2011*2012/2011
=1/2*2012/2011
=1006/2011
=(1-1/2)(1+1/2)(1-1/3)(1+1/3)(1-1/4)(1+1/4)*.(1-1/2010)(1+1/2010)(1-1/2011)(1+1/2011)
=1/2*3/2*2/3*4/3*3/4*5/4*.2009/2010*2011/2010*2010/2011*2012/2011
=1/2*2012/2011
=1006/2011