(1-½²)(1-⅓²)(1-¼²)……(1-1/100²)
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![(1-½²)(1-⅓²)(1-¼²)……(1-1/100²)](/uploads/image/z/657675-27-5.jpg?t=%EF%BC%881-%26%23189%3B%26%23178%3B%EF%BC%89%EF%BC%881-%26%238531%3B%26%23178%3B%EF%BC%89%EF%BC%881-%26%23188%3B%26%23178%3B%EF%BC%89%E2%80%A6%E2%80%A6%EF%BC%881-1%EF%BC%8F100%26%23178%3B%EF%BC%89)
(1-½²)(1-⅓²)(1-¼²)……(1-1/100²)
(1-½²)(1-⅓²)(1-¼²)……(1-1/100²)
(1-½²)(1-⅓²)(1-¼²)……(1-1/100²)
(1-½²)(1-⅓²)(1-¼²)……(1-1/100²)
=(1-1/2)(1+1/2)(1-1/3)(1+1/3)(1-1/4)(1+1/4)...(1-1/100)(1+1/100)
=1/2x3/2x2/3x4/3x3/4x5/4.x99/100x101/100
=1/2x1x1.x1x101/100
=101/200
原式=(1-1/2)(1+1/2)(1-1/3)(1+1/3)(1-1/4)(1+1/4)...(1-1/99)(1+1/99))(1-1/100)(1+1/100)
=1/2 *3/2 *2/3 *4/3 *3/4* 5/4....* 98/99*100/99 * 99/100 *101/100
=1/2 * 101/100
=101/200
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