(1-1/2²)×(1-1/3²)×(1-1/4²)…(1-1/2007²)×(
来源:学生作业帮 编辑:作业帮 分类:数学作业 时间:2024/05/27 20:56:49
(1-1/2²)×(1-1/3²)×(1-1/4²)…(1-1/2007²)×(1-1/2008²)
(1-1/2²)×(1-1/3²)×(1-1/4²)…(1-1/2007²)×(1-1/2008²)
=((1-1/2)×(1-1/3)×(1-1/4)×…×(1-1/2007)×(1-1/2008))×((1+1/2)×(1+1/3)×(1+1/4)×…×(1+1/2007)×(1+1/2008))
=(1/2×2/3×3/4…2006/2007×2007/2008)×(3/2×4/3×5/4…2008/2007×2009/2008)
=(1/2008)×(2009/2)
=2009/4016
=((1-1/2)×(1-1/3)×(1-1/4)×…×(1-1/2007)×(1-1/2008))×((1+1/2)×(1+1/3)×(1+1/4)×…×(1+1/2007)×(1+1/2008))
=(1/2×2/3×3/4…2006/2007×2007/2008)×(3/2×4/3×5/4…2008/2007×2009/2008)
=(1/2008)×(2009/2)
=2009/4016
1²-2²+3²-4²……+2005²-2006²+2007
初二数学题(1-1/2²)(1-1/3²)(1-1/4²)…(1-1/9²)(1
(1-1/2²)(1-1/3²)(1-1/4²)……(1-1/10²)
(1-1/2²)(1-1/3²)(1-1/4²)……*(1-1/2008²)
求和:1²-2²+3²-4²+5²-6²+…+99²
1²-2²+3²-4²+.+2007²-2008²
计算:1-2²+3²-4²+5²-6²+...+2007²-
1²+2²+3²+4²+5²
(1²+3²+5²+……+99²)-(2²+4²+6
1²-2²+3²-4²+……+99²-100²怎么计算?
求值(2²+4²+6²+……+2000²)-(1²+3²+5
1²-2²+3²-4²+5²-6²+7²-8