计算:(1-1/2²)(1-1/3²)(1-1/4²)x...x(1-1/19²)(1-1/20²)
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![计算:(1-1/2²)(1-1/3²)(1-1/4²)x...x(1-1/19²)(1-1/20²)](/uploads/image/z/364408-16-8.jpg?t=%E8%AE%A1%E7%AE%97%EF%BC%9A%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%89x...x%281%EF%BC%8D1%2F19%26%23178%3B%29%281%EF%BC%8D1%2F20%26%23178%3B%29)
计算:(1-1/2²)(1-1/3²)(1-1/4²)x...x(1-1/19²)(1-1/20²)
计算:(1-1/2²)(1-1/3²)(1-1/4²)x...x(1-1/19²)(1-1/20²)
计算:(1-1/2²)(1-1/3²)(1-1/4²)x...x(1-1/19²)(1-1/20²)
平方差
=(1-1/2)(1+1/2)(1-1/3)(1+1/3)……(1-1/20)(1+1/20)
=(1/2)(3/2)(2/3)(4/3)……(19/20)(21/20)
中间约分
=(1/2)(21/20)
=21/40