Understanding the Equation (2n-1)! = (2n-1)(2n)(2n-1)!

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In summary, the formula (2n-1)! = (2n-1)(2n)(2n-1)! is not true, but the formula (2n+1)!= (2n+1)(2n)(2n-1)! is true. This is because of the definition of factorial, where (2n+1)!= (2n+1)(2n)(2n-1)(2n-2)(2n-3)(2n-4)...(3)(2)(1) and (2n-1)!= (2n-1)(2n-3)(2n-4)...(3)(2)(1), the "tail end" of the first product. Therefore
  • #1
fiziksfun
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Can someone please explain to me why (2n-1)! = (2n-1)(2n)(2n-1)! ?? I'm very confused.
 
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  • #2


It doesn't. Did this come from a book?
 
  • #3


Do you mean (2n)!= (2n)(2n-1)! ? If so, it comes from the definition of factorial: (2n)!=(2n)(2n-1)(2n-2)...(1)
and (2n-1)!=(2n-1)(2n-2)...(1) so (2n)(2n-1)!=(2n)(2n-1)(2n-2)...(1)=(2n)!
 
  • #4


fiziksfun said:
Can someone please explain to me why (2n-1)! = (2n-1)(2n)(2n-1)! ?? I'm very confused.
Yes, you are! Dividing both sides of your formula by (2n-1)! you get 1= (2n-1)(2n) which is NOT true!

Perhaps you mean (2n+1)!= (2n+1)(2n)(2n-1)!. That's true because, by definition, (2n+1)!= (2n+1)(2n)(2n-1)(2n-2)(2n-3)(2n-4)...(3)(2)(1). And (2n-1)!= (2n-1)(2n-3)(2n-4)...(3)(2)(1), the "tail end" of that first product. so (2n+1)!= (2n+1)(2n)(2n-1)!
 

Related to Understanding the Equation (2n-1)! = (2n-1)(2n)(2n-1)!

1. What does "2n-1" mean in the context of solving a problem?

The expression "2n-1" represents a mathematical formula where n is a variable. This means that the value of the expression will change depending on the value of n that is substituted. In order to solve this expression, we must find the value of n that makes the equation true.

2. Why is "2n-1" commonly used in scientific calculations?

The expression "2n-1" is useful in scientific calculations because it allows for a wide range of numbers to be represented. By using a variable (n) instead of a specific number, the expression can apply to any value that is substituted for n. This makes it a versatile tool in solving various mathematical problems.

3. How do you solve "2n-1" for a specific value of n?

To solve "2n-1" for a specific value of n, we must plug in the given value for n into the expression and perform the necessary operations. For example, if n=3, then we would solve 2(3)-1, which would equal 5. This means that when n=3, the value of "2n-1" is 5.

4. Can "2n-1" be simplified further?

Yes, "2n-1" can be simplified further depending on the context of the problem. For example, if the expression is part of a larger equation, it may be possible to combine like terms or use other mathematical principles to simplify it. However, "2n-1" itself cannot be simplified any further without more information.

5. What are some real-world applications of "2n-1"?

"2n-1" has many real-world applications, particularly in the fields of mathematics, science, and engineering. It can be used to calculate probabilities, solve equations, find the area of geometric shapes, and much more. It is also commonly used in computer programming as it allows for a range of values to be represented by a single expression.

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