初二数学题(1-1/2²)(1-1/3²)(1-1/4²)…(1-1/9²)(1
来源:学生作业帮 编辑:搜搜做题作业网作业帮 分类:数学作业 时间:2024/07/06 14:50:27
初二数学题(1-1/2²)(1-1/3²)(1-1/4²)…(1-1/9²)(1-1/10²)
![初二数学题(1-1/2²)(1-1/3²)(1-1/4²)…(1-1/9²)(1](/uploads/image/z/4088524-4-4.jpg?t=%E5%88%9D%E4%BA%8C%E6%95%B0%E5%AD%A6%E9%A2%98%281-1%2F2%26%23178%3B%29%281-1%2F3%26%23178%3B%29%281-1%2F4%26%23178%3B%29%E2%80%A6%281-1%2F9%26%23178%3B%29%281)
(1-1/2²)(1-1/3²)(1-1/4²)…(1-1/9²)(1-1/10²)
连续运用平方差
=(1-1/2)×(1+1/2)×(1-1/3)×(1+1/3)×……×(1-1/10)×(1+1/10)
=1/2×3/2×2/3×4/3×……×11/10
=1/2×11/10
=11/20
连续运用平方差
=(1-1/2)×(1+1/2)×(1-1/3)×(1+1/3)×……×(1-1/10)×(1+1/10)
=1/2×3/2×2/3×4/3×……×11/10
=1/2×11/10
=11/20