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25 March, 05:03

Write an equation for the sequence: 2, 24, 720, 40320, 3628800

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  1. 25 March, 05:26
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    The sequence forms a group of factorials.

    Notice that

    2! = 2

    4! = 24

    6! = 720

    8! = 40320

    10! = 3628800

    Each number beside a factorial is an even number. The equation for even number is 2x. Therefore, the final equation is

    f (x) = 2x!

    Verify

    x = 1, f (1) = 2 (1) ! = 2!

    x = 2, f (2) = 2 (2) ! = 4!

    x = 3, f (3) = 2 (3) ! = 6!

    and so on.
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