Multiplication of odd numbers 1 to 99?

How do I work out the product all the odd numbers from 1 to 99, giving the answer in terms of factorials

2 Answers

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  • 9 years ago
    Favorite Answer

    I will use P(1 - n) to mean the product of numbers from 1 to n.

    You want to find P(1 ∙ 3 ∙ 5 ∙ 7 . . . . . 99)

    which is obviously

    99! - P (2 ∙ 4 ∙ 6 ∙ 8 . . . . . 98)

    = 99! - P(1 ∙ 2 ∙ 3 ∙ 4 ∙ . . . . .49) ∙ 2^49 . . . . . (take out a factor of 2 from each of 2, 4, 6, etc.)

    = 99! - (49!) (2^49)

  • Ron W
    Lv 7
    9 years ago

    Observe that

    1*3*5*...*97*99 = 1*2*3*...*97*98*99/(2*4*6*...*96*98)

    The denominator may be factored as 2^49(1*2*3*...*48*49)

    so

    1*3*5*...*97*99 = 99!/(2^49 * 49!)

    The number itself is

    2725 39213 97507 29502 98071 32454 00918 63329 07963 30545 80341 37343 28823 44310 62011 71875

    according to Mathematica.

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