(1-1/11²)*(1-1/12²)*……*(1-1/99²)
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![(1-1/11²)*(1-1/12²)*……*(1-1/99²)](/uploads/image/z/635982-6-2.jpg?t=%281-1%2F11%26%23178%3B%29%2A%281-1%2F12%26%23178%3B%29%2A%E2%80%A6%E2%80%A6%2A%281-1%2F99%26%23178%3B%29)
(1-1/11²)*(1-1/12²)*……*(1-1/99²)
(1-1/11²)*(1-1/12²)*……*(1-1/99²)
(1-1/11²)*(1-1/12²)*……*(1-1/99²)
平方差
原式=(1-1/11)(1+1/11)(1-1/12)(1+1/12)……(1-1/99)(1+1/99)
=(10/11)(12/11)(11/12)(13/12)……(98/99)(100/99)
中间约分
=(10/11)(100/99)
=1000/1089