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# 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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- ignoramusLv 79 years agoFavorite 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 WLv 79 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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