Proving an equality using induction proof not working

[tony700]

Homework Statement

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

Homework Equations

The Attempt at a Solution

 

[pizzasky]

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 $\prod\limits_{n=1}^{k+1}n(2(k+1)+2-2n)=2^{k+1}((k+1)!)^2$.

 

[SammyS]

Homework Statement

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

Homework Equations

The Attempt at a Solution

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.

 

[Ray Vickson]

Homework Statement

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

Homework Equations

The Attempt at a Solution

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.