Maths Proof - Help!

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

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

Couldnt you just do it by induction?

\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...

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!)

(edited 7 years ago)

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.

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.

It was actually meant to be 2^n

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