N=0 vs N=1 in Homework Equations: What's the Difference?

[illidari]

Homework Statement

Homework Equations

The Attempt at a Solution

I have the same final answer except without the X/2 + power series(n=1), I just have the same power series except its n=0.

Is there any reason why they are pulling out n=0 and changing it to n=1?

I did a similar problem which seems I could do the same thing but they left it as n=0.

 

[vela]

The product in the numerator, 1x3x5x...x(2n-1), doesn't really work out for n=0.