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

  • Thread starter Baou
  • Start date
In summary, the conversation was about writing a power series expansion for a function and expressing 2*4*6*8... mathematically. The solution was to use a product notation, \prod_{n=1}^{\infty} 2x.
  • #1
Baou
6
0

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: [tex]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}...[/tex]


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?
 
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  • #2
Hint: 2*4*6=23*1*2*3 :wink:
 
  • #3
Damnit, I knew it'd be something simple... =P Well, thanks for the help!
 
  • #4
ƒ(x) said:
I believe what you're looking for is...

[tex]\prod[/tex] 2x from 1 to infinity

Why would you think this?:confused:

[tex]\prod_{n=1}^{\infty} 2x=\infty[/tex]
 
  • #5
gabbagabbahey said:
Why would you think this?:confused:

[tex]\prod_{n=1}^{\infty} 2x=\infty[/tex]

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)
 

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

What is the mathematical expression for multiplying consecutive even numbers?

The mathematical expression for multiplying consecutive even numbers is 2n, where n represents the number of even numbers being multiplied together. For example, 2*4*6*8 can be written as 2^4, where n=4.

How do you express the product of consecutive even numbers using factorial notation?

The product of consecutive even numbers can be expressed using factorial notation as n!, where n represents the number of even numbers being multiplied together. For example, 2*4*6*8 can be written as 4!, where n=4.

Can the expression for multiplying consecutive even numbers be simplified?

Yes, the expression for multiplying consecutive even numbers can be simplified using exponent notation. Instead of writing out each individual even number, you can write the expression as 2^n, where n represents the number of even numbers being multiplied together. For example, 2*4*6 can be written as 2^3, where n=3.

How can you use summation notation to express the product of consecutive even numbers?

To use summation notation, you can write the expression as a summation of all the even numbers being multiplied together. For example, 2*4*6*8 can be written as ∑(2n), where n ranges from 1 to 4. This is equivalent to writing 2*4*6*8.

Can the expression for multiplying consecutive even numbers be applied to any number of even numbers?

Yes, the expression 2n can be applied to any number of even numbers being multiplied together. It is a general formula that can be used to express the product of consecutive even numbers. However, it is important to note that the value of n will vary depending on the number of even numbers being multiplied together.

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