(1-1/2²)(1-1/3²)…(1-1/2011²)(1-1/2012²)

2个回答

  • (1-1/2^2)(1-1/3^2)(1-1/4^2)···(1-1/n^2)···(1-1/100^2)

    =(i=2,100)∏(1-1/i^2)

    =(i=2,100)∏[(1+1/i)(1-1/i)]

    =(i=2,100)∏(1+1/i)×(i=2,100)∏(1-1/i)

    =[(3/2)×(4/3)×(5/4)×···×(101/100)]

    ×[(1/2)×(2/3)×(3/4)×···×(99/100)]

    =(101/2)×(1/100)

    =101/200

    ____∏是求积符合,和求和符号∑是一样的!用∏,可以节约很多笔墨,思路清晰,不易出错,用它好啊