Proving a Simple Formula for n = 2,4,6,8 Using Mathematical Induction

[duki]

Homework Statement

Conjecture a simple formula for n = 2,4,6,8

Homework Equations

Kind of...
$$Tn = (1-\frac{1}{n^2})(1-\frac{1}{(n-1)^2})... to n=1$$

The Attempt at a Solution

The pattern is 3/4, 5/8, 7/12, 9/16
I know that the top is increasing by 2 and the bottom is increasing by 4... but I don't know how to put that into a formula to which I can prove.

Thanks for any help!

 

[duki]

oooooh snap, how about this:

$$Tn = \frac{n+1}{n*2}$$ for all even n?

 

[Dick]

Why not?