Reducing Factorials: Is the Answer 1/[2n*2n+1]?

Thread starter pugfug90
Start date Apr 18, 2007
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Factorial Simplifying

In summary, a factorial is a mathematical operation that multiplies a number by all of the positive integers smaller than it, resulting in a large number represented by an exclamation mark (!) after the original number. Simplifying a factorial can make it easier to use in calculations and to understand its value, as well as reducing the number of terms in an expression. To simplify a factorial, you can use the basic factorial rule or algebraic rules. Some common mistakes when simplifying a factorial include forgetting to include all smaller positive integers and not properly applying the factorial rule or algebraic rules. Not every factorial can be simplified, such as prime factorials, but they can still be written in their factorial form using the exclamation mark notation.

Apr 18, 2007

pugfug90

Homework Statement

(2n-1)!/(2n+1)!

Homework Equations

The Attempt at a Solution

...2n-2*2n-1
------------ (pretend that's a divider)
...2n-2*2n-1*2n*2n+1

Is the answer 1/[2n*2n+1]?

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Apr 18, 2007

Dick

Science Advisor

Homework Helper

It sure is.

Apr 19, 2007

HallsofIvy

Science Advisor

Homework Helper

But it would look better with an additional pair of parentheses:
1/[2n(2n+1)]. I would have been inclined to interpret what you have as
1/(2n²+1).

Apr 19, 2007

pugfug90

Thanks :)

Related to Reducing Factorials: Is the Answer 1/[2n*2n+1]?

What is a factorial?

A factorial is a mathematical operation that multiplies a number by all of the positive integers smaller than it, resulting in a large number represented by an exclamation mark (!) after the original number.

Why is it important to simplify a factorial?

Simplifying a factorial can make it easier to use in calculations and to understand its value. It also helps to reduce the number of terms in an expression.

How do you simplify a factorial?

To simplify a factorial, you can use the basic factorial rule: n! = n * (n-1) * (n-2) * ... * 2 * 1. You can also use algebraic rules to simplify factorials in equations and expressions.

What are some common mistakes when simplifying a factorial?

One common mistake when simplifying a factorial is forgetting to include all the smaller positive integers in the multiplication. Another mistake is not properly applying the factorial rule or algebraic rules.

Can every factorial be simplified?

Not every factorial can be simplified. Some factorials, such as prime factorials, cannot be simplified any further. However, they can still be written in their factorial form using the exclamation mark notation.