How can I simplify this factorial expression?

Thread starter Flappy
Start date Dec 9, 2008
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Factorial

In summary, a factorial is a mathematical operation denoted by the exclamation point symbol (!) that finds the product of all positive integers from 1 up to a given number. To simplify a factorial, a formula can be used where the given number is multiplied by the number one less than it, and so on until reaching 1. There is also a shortcut for simplifying smaller factorials. Simplifying factorials is important for solving problems in probability, combinatorics, and other areas of mathematics, as well as understanding more complex operations and equations.

Dec 9, 2008

Flappy

Homework Statement

[tex] \frac{(kn)!}{(kn+k)!} [/tex]

I was thinking:

(kn)! = 1*2*3...(kn)
(kn+k)! = 1*2*3...(kn)(kn+k)

and I would be left with 1/kn+k

But my book has the answer as:
[tex] \frac{1}{(kn+k)(kn+k-1)...(kn+1)} [/tex]

How can I arrive to that?

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Dec 9, 2008

mutton

There are k numbers between kn and kn + k, not just one.

1. What is a factorial?

A factorial is a mathematical operation denoted by the exclamation point (!) symbol. It is used to find the product of all positive integers from 1 up to a given number. For example, 5! (read as "five factorial") is equal to 5 x 4 x 3 x 2 x 1 = 120.

2. How do you simplify a factorial?

To simplify a factorial, you can use the following formula: n! = n x (n-1) x (n-2) x ... x 2 x 1. This means that you start with the given number and multiply it by the number one less than it, then by the number two less than it, and so on until you reach 1.

3. Can you give an example of a simplified factorial?

Sure, let's say we want to simplify 7!. Using the formula above, we get: 7! = 7 x 6 x 5 x 4 x 3 x 2 x 1 = 5040. So 7! is equal to 5040.

4. Are there any shortcuts for simplifying factorials?

Yes, there is a shortcut when the given number is a smaller factorial. For example, if we want to simplify 4!, we can use the formula 4! = 4 x 3 x 2 x 1 = 24. But we can also use the fact that 4! is equal to 3! x 4, so we can simply multiply 3! (which is equal to 3 x 2 x 1 = 6) by 4, giving us the same result of 24.

5. Why is simplifying factorials important?

Simplifying factorials can help us solve problems in probability, combinatorics, and other areas of mathematics. It also allows us to express large numbers in a more manageable and concise way. Additionally, it is a fundamental concept in understanding more complex mathematical operations and equations.