(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

So we have to prove that [itex]\frac{(n+1)(n+2)(n+3)...(2n)}{1*3*5...*(2n-1)}[/itex] = 2^{n}

2. The attempt at a solution

I. For n=1, obviously the proposition is true. (2*1/(2-1) = 2^1 = 2)

II. Let n=k and assume [itex]\frac{(k+1)(k+2)(k+3)...(2k)}{1*3*5...*(2k-1)}[/itex] = 2^{k}.

Now, for n=k+1 we have: 2^{k}* [itex]\frac{(2k +2)}{2k+1)}[/itex] = 2^{k+1}→ 2^{(k+1)}*[itex]\frac{(k+1)}{2k+1)}[/itex] = 2^{k+1}. Which is not true.

So, I cannot figure out what am I doing wrong.

Thanks in advance...

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# Proof by Induction Problem

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