(1-1/2²)×(1-1/3²)×…×(1-1/2009²)×(1-1/2010²)1-1/2²=1/2×3/2,1-1/3²=2/3×4/3,以此类推……
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![(1-1/2²)×(1-1/3²)×…×(1-1/2009²)×(1-1/2010²)1-1/2²=1/2×3/2,1-1/3²=2/3×4/3,以此类推……](/uploads/image/z/5294081-65-1.jpg?t=%EF%BC%881-1%2F2%26%23178%3B%EF%BC%89%C3%97%EF%BC%881-1%2F3%26%23178%3B%EF%BC%89%C3%97%E2%80%A6%C3%97%EF%BC%881-1%2F2009%26%23178%3B%EF%BC%89%C3%97%EF%BC%881-1%2F2010%26%23178%3B%EF%BC%891-1%2F2%26%23178%3B%3D1%2F2%C3%973%2F2%2C1-1%2F3%26%23178%3B%3D2%2F3%C3%974%2F3%2C%E4%BB%A5%E6%AD%A4%E7%B1%BB%E6%8E%A8%E2%80%A6%E2%80%A6)
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(1-1/2²)×(1-1/3²)×…×(1-1/2009²)×(1-1/2010²)1-1/2²=1/2×3/2,1-1/3²=2/3×4/3,以此类推……
(1-1/2²)×(1-1/3²)×…×(1-1/2009²)×(1-1/2010²)
1-1/2²=1/2×3/2,1-1/3²=2/3×4/3,以此类推……
(1-1/2²)×(1-1/3²)×…×(1-1/2009²)×(1-1/2010²)1-1/2²=1/2×3/2,1-1/3²=2/3×4/3,以此类推……
(1-1/2²)×(1-1/3²)×…×(1-1/2009²)×(1-1/2010²)
=1/2×3/2×2/3×4/3×…×2008/2009×2010/2009×2009/2010×2011/2010
=1/2×2011/2010
=2011/4020