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Math Help - Find the Product

  1. #1
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    Find the Product

    I need to find the product:

    (1-1/2)(1-1/3)(1-1/4)(1-1/5)......(1-1/499)(1-1/500) =

    NOTICE: The list goes from (1-1/2) all the way to
    (1 - 1/500).

    How do I solve this question?

    How do I find the product?
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  2. #2
    Like a stone-audioslave ADARSH's Avatar
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    Quote Originally Posted by magentarita View Post
    I need to find the product:

    (1-1/2)(1-1/3)(1-1/4)(1-1/5)......(1-1/499)(1-1/500) =

    NOTICE: The list goes from (1-1/2) all the way to
    (1 - 1/500).

    How do I solve this question?

    How do I find the product?
    1-1/2 = 1/2

    1-1/3 = 2/3

    1-1/4 = 3/4

    1-1/5 =4/5

    .
    .
    .

    1-(1/499) = 498/499

    1-(1/500) = 499/500

    Multiply all these terms

    \frac{1 * 2 * 3 * 4* 5.....499}{2*3*4*5...499*500}

    cancel common terms in numerator and denominator.

    Ans = 1/500
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  3. #3
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    e^(i*pi)'s Avatar
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    1
    Quote Originally Posted by ADARSH View Post
    1-1/2 = 1/2

    1-1/3 = 2/3

    1-1/4 = 3/4

    1-1/5 =4/5

    .
    .
    .

    1-(1/499) = 498/499

    1-(1/500) = 499/500

    Multiply all these terms

    \frac{1 * 2 * 3 * 4* 5.....499}{2*3*4*5...499*500}

    cancel common terms in numerator and denominator.

    Ans = 1/500
    Indeed you do. For n terms this will be

    \frac{(n-1)!}{n!} = \frac{1}{n}
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  4. #4
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    tell me

    Quote Originally Posted by ADARSH View Post
    1-1/2 = 1/2

    1-1/3 = 2/3

    1-1/4 = 3/4

    1-1/5 =4/5

    .
    .
    .

    1-(1/499) = 498/499

    1-(1/500) = 499/500

    Multiply all these terms

    \frac{1 * 2 * 3 * 4* 5.....499}{2*3*4*5...499*500}

    cancel common terms in numerator and denominator.

    Ans = 1/500
    How do I use the formula (1 - n)!/n! = 1/n to find the same answer?
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  5. #5
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    tell me...

    Quote Originally Posted by e^(i*pi) View Post
    Indeed you do. For n terms this will be

    \frac{(n-1)!}{n!} = \frac{1}{n}

    How do I use the formula (1 - n)!/n! = 1/n to find the same answer?
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  6. #6
    Like a stone-audioslave ADARSH's Avatar
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    Quote Originally Posted by magentarita View Post
    How do I use the formula (1 - n)!/n! = 1/n to find the same answer?
    Your formula is not correct




    =\frac{(500-1)(500-2).....(2)(1)}{(500)(499)...(2)(1)}

    =\frac{(500-1)!}{500!}

    =\frac{(499)!}{500!}

    Remember that (n-1)! is not equal to (1-n)!

    =\frac{(n-1)!}{n!} = \frac{1}{n} {\color{red}\ne} \frac{(1-n)!}{n!}

    =\frac{1}{500}
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  7. #7
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    I see...

    Quote Originally Posted by ADARSH View Post
    Your formula is not correct




    =\frac{(500-1)(500-2).....(2)(1)}{(500)(499)...(2)(1)}

    =\frac{(500-1)!}{500!}

    =\frac{(499)!}{500!}

    Remember that (n-1)! is not equal to (1-n)!

    =\frac{(n-1)!}{n!} = \frac{1}{n} {\color{red}\ne} \frac{(1-n)!}{n!}

    =\frac{1}{500}
    I see what I did wrong.
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