(1-1/2²)(1-1/3²)(1-1/4²)…(1-1/2013²)
来源:学生作业帮助网 编辑:作业帮 时间:2024/06/27 09:50:03
![(1-1/2²)(1-1/3²)(1-1/4²)…(1-1/2013²)](/uploads/image/z/2590196-68-6.jpg?t=%EF%BC%881%EF%BC%8D1%2F2%26%23178%3B%EF%BC%89%EF%BC%881%EF%BC%8D1%2F3%26%23178%3B%EF%BC%89%EF%BC%881%EF%BC%8D1%2F4%26%23178%3B%EF%BC%89%E2%80%A6%EF%BC%881%EF%BC%8D1%2F2013%26%23178%3B%EF%BC%89)
(1-1/2²)(1-1/3²)(1-1/4²)…(1-1/2013²)
(1-1/2²)(1-1/3²)(1-1/4²)…(1-1/2013²)
(1-1/2²)(1-1/3²)(1-1/4²)…(1-1/2013²)
原式=1/2×3/2×2/3×4/3×3/4×……×2012/2013×2014/2013
=1/2×2014/2013
=1007/2013