因式分解(1-1/2²)(1-1/3²)(1-1/4²)…(1-1/9²)(1-
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因式分解(1-1/2²)(1-1/3²)(1-1/4²)…(1-1/9²)(1-1/10²)
![因式分解(1-1/2²)(1-1/3²)(1-1/4²)…(1-1/9²)(1-](/uploads/image/z/15720295-31-5.jpg?t=%E5%9B%A0%E5%BC%8F%E5%88%86%E8%A7%A3%EF%BC%881-1%EF%BC%8F2%26%23178%3B%EF%BC%89%EF%BC%881-1%EF%BC%8F3%26%23178%3B%EF%BC%89%281-1%EF%BC%8F4%26%23178%3B%29%E2%80%A6%281-1%EF%BC%8F9%26%23178%3B%29%281-)
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)……(9/10)(11/10)
中间约分
=(1/2)(11/10)
=11/20
=(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)……(9/10)(11/10)
中间约分
=(1/2)(11/10)
=11/20