(1-1/2²)(1-1/3²)…(1-1/9²)(1-1/10²)
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:2024/07/24 08:35:00
(1-1/2²)(1-1/3²)…(1-1/9²)(1-1/10²)
![(1-1/2²)(1-1/3²)…(1-1/9²)(1-1/10²)](/uploads/image/z/1918556-44-6.jpg?t=%EF%BC%881-1%2F2%26%23178%3B%EF%BC%89%EF%BC%881-1%2F3%26%23178%3B%EF%BC%89%E2%80%A6%EF%BC%881-1%2F9%26%23178%3B%EF%BC%89%EF%BC%881-1%2F10%26%23178%3B%EF%BC%89)
( 1-1/2方)(1-1/3方)(1-1/4方)...(1-1/9方)(1-1/10方)
=(1-1/2)(1+1/2)(1-1/3)(1+1/3)(1-1/4)(1+1/4)...(1-1/9)(1+1/9)(1-1/10)(1+1/10)
=(1/2)(3/2)(2/3)(4/3)(3/4)(5/4)...(8/9)(10/9)(9/10)(11/10)
=(1/2)(11/10)
=11/10
运用平方差公式分解!
=(1-1/2)(1+1/2)(1-1/3)(1+1/3)(1-1/4)(1+1/4)...(1-1/9)(1+1/9)(1-1/10)(1+1/10)
=(1/2)(3/2)(2/3)(4/3)(3/4)(5/4)...(8/9)(10/9)(9/10)(11/10)
=(1/2)(11/10)
=11/10
运用平方差公式分解!
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