Expressing 2*4*6*8*10*etc. mathematically

[Baou]

Homework Statement

This doesn't seem too hard but I can't figure it out. I'm trying to write out a power series expansion for a function, and after a bit of math I've got: $$f\left(x\right) = 1 - \frac32 + \frac98 - \frac{27}{48} + \frac{81}{384}... = 1 - \frac{3^1}2 + \frac{3^2}{2*4} - \frac{3^3}{2*4*6} + \frac{3^4}{2*4*6*8}...$$

Homework Equations

N/A

The Attempt at a Solution

I just don't know how to express 2*4*6*8...etc. mathematically. Help please?

 

[gabbagabbahey]

Hint: 2*4*6=2³*1*2*3

 

[Baou]

Damnit, I knew it'd be something simple... =P Well, thanks for the help!

 

[gabbagabbahey]

I believe what you're looking for is...

$$\prod$$ 2x from 1 to infinity

Why would you think this?

$$\prod_{n=1}^{\infty} 2x=\infty$$

 

[ƒ(x)]

Why would you think this?

$$\prod_{n=1}^{\infty} 2x=\infty$$

Its late and I'm tired. Dont mind me.

I thought he was just asking how can you express 2*4*8... (I only read the title)