# Proving an equality using induction proof not working

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1. Jan 3, 2016

### tony700

1. The problem statement, all variables and given/known data
I work out the problem completely and it does not equal out. Having problems with two variable induction proofs (n and k) in this problem. Below is as far as I got, jpeg below

2. Relevant equations

3. The attempt at a solution

#### Attached Files:

• ###### induction.jpg
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2. Jan 3, 2016

Our inductive hypothesis is $\prod\limits_{n=1}^{k}n(2k+2-2n)=2^k(k!)^2$, for some $k\in\{1,2,...\}$.

We want to show that $\prod\limits_{n=1}^{k+1}n(2(k+1)+2-2n)=2^{k+1}((k+1)!)^2$.

3. Jan 3, 2016

### SammyS

Staff Emeritus

That's what you're to prove.

I think it's clearer if you do the induction step as follows.

Assume that $\displaystyle \ \prod_{n=1}^{k}n(2k+2-2n)=2^k(k!)^2 \$ is true for $\ k=m\$ for some $m>0$. Then show that it's true for $k = m+1$. You must replace every $k$ with $m$ or $m+1$ as appropriate.

Note: In the jpeg image that you showed, you needed to have extra parentheses in a number of places.

4. Jan 3, 2016

### Ray Vickson

Are you absolutely required to use induction? If not, just writing out the product directly and simplifying is by far the easiest way to do the problem.