# Mathematical Induction

1. Jan 25, 2009

### duki

1. The problem statement, all variables and given/known data

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

2. Relevant equations

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

3. 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!

Last edited: Jan 25, 2009
2. Jan 25, 2009

### duki

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

3. Jan 25, 2009

Why not?