(1-1/2)x(1+1/2)x(1-1/3)x(1+1/3)x.x(1-1/99)x(1+1/99)结果是等于50/9

3个回答

  • 如果自己接受不了,可就先别算那么长,一节节算算,找找规律

    (1-1/2) X (1+1/2) X (1-1/3) X (1+1/3)

    = 1/2 X 3/2 X 2/3 X 4/3

    = 1/2 X 1 X 4/3

    = 2/3

    (1-1/2) X (1+1/2) X (1-1/3) X (1+1/3) X (1-1/4) X (1+1/4)

    = 1/2 X 3/2 X 2/3 X 4/3 X 3/4 X 5/4

    = 1/2 X 1 X 1 X 5/4

    = 5/8

    同理,题目就是

    (1-1/2) X (1+1/2) X (1-1/3) X …… X (1+1/98) X (1-1/99) X (1+1/99)

    = 1/2 X 3/2 X 2/3 X …… X 99/98 X 98/99 X 100/99

    = 1/2 X 1 X 1 X …… X 1 X 100/99

    = 50/99