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Maths Proof - Help!

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    Show that the product of the first n even positive integers is 2n(n!). [Hint: you can do it in one line.]

    Please help! lol
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    (Original post by Higherdude)
    Show that the product of the first n even positive integers is 2n(n!). [Hint: you can do it in one line.]

    Please help! lol
     \displaystyle 1 \times 2 \times 3 \times 4 \times... \times n = n!

    thats your starting point
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    Couldnt you just do it by induction?
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    (Original post by DylanJ42)
     \displaystyle 1 \times 2 \times 3 \times 4 \times... \times n = n!

    thats your starting point
    I have done this, and I have also used 2x4x6x8...x2n

    But I don't know what to do after that...
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    (Original post by Higherdude)
    I have done this, and I have also used 2x4x6x8x2n

    But I don't know what to do after that...
      \displaystyle 1 \times 2 \times 3 \times 4 \times... \times n = n!

     \displaystyle 2 \times 4 \times 6 \times 8 \times... \times 2n = \displaystyle 2(1) \times 2(2) \times 2(3) \times 2(4) \times... \times 2(n)

    now take all those 2s at the front of the brackets to the front and get

     \displaystyle 2^n \times  1 \times 2 \times 3 \times 4 \times... \times n =  \displaystyle 2^n(n!)
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    (Original post by an_atheist)
    Couldnt you just do it by induction?
    Lol a bit overkill. It trivially follows from the definition of factorial, as DylanJ42 showed.
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    (Original post by IrrationalRoot)
    Lol a bit overkill. It trivially follows from the definition of factorial, as DylanJ42 showed.
    But it is possible. If you cannot think of a place to start, then it is as valid a thing to try as any.
    Very lengthy though it may be.
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    It was actually meant to be 2^n
 
 
 
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