计算:(1-1/2²)(1-1/3²)......(1-1/2004²)(1-1/2005
来源:学生作业帮 编辑:搜搜做题作业网作业帮 分类:政治作业 时间:2024/08/15 14:22:46
计算:(1-1/2²)(1-1/3²)......(1-1/2004²)(1-1/2005²)
![计算:(1-1/2²)(1-1/3²)......(1-1/2004²)(1-1/2005](/uploads/image/z/17839332-36-2.jpg?t=%E8%AE%A1%E7%AE%97%EF%BC%9A%EF%BC%881-1%2F2%26%23178%3B%EF%BC%89%EF%BC%881-1%2F3%26%23178%3B%EF%BC%89......%EF%BC%881-1%2F2004%26%23178%3B%EF%BC%89%EF%BC%881-1%2F2005)
(1-1/2²)(1-1/3²)......(1-1/2004²)(1-1/2005²)
=(1-1/2)(1+1/2)(1-1/3)(1+1/3).(1-1/2005)(1+1/2005)
=1/2×3/2×2/3×4/3×...×2004/2005×2006/2005
=1/2×2/3×3/4×...×2004/2005×3/2×4/3×...×2006/2005
=1/2005×2006/2
=1003/2005;
手机提问的朋友在客户端右上角评价点【满意】即可.
=(1-1/2)(1+1/2)(1-1/3)(1+1/3).(1-1/2005)(1+1/2005)
=1/2×3/2×2/3×4/3×...×2004/2005×2006/2005
=1/2×2/3×3/4×...×2004/2005×3/2×4/3×...×2006/2005
=1/2005×2006/2
=1003/2005;
手机提问的朋友在客户端右上角评价点【满意】即可.