Evaluate Limit with Factorials: \lim_{n \to \infty}

Thread starter pseudogenius
Start date Apr 8, 2010
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Factorials Limit

In summary, a limit with factorials is a mathematical concept that describes the behavior of a sequence of numbers as the input value approaches infinity. It takes into account the factorial function and can result in different behaviors and values compared to regular limits. Common techniques for evaluating limits with factorials include using the ratio test, root test, or comparison test. A limit with factorials exists if the sequence converges to a specific value or approaches infinity/negative infinity, and can sometimes be evaluated without mathematical techniques by recognizing patterns or simplifying the sequence.

Apr 8, 2010

pseudogenius

Anyone know of any method to evaluate this limit,

[tex]\lim_{n \to \infty} \frac{n!}{\left(\frac{n+p}{2}\right)!\left(\frac{n-p}{2}\right)!}2^{-n}[/tex]

it seems to go to zero, but I have no way to be sure.

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Apr 8, 2010

Hurkyl

Staff Emeritus

Science Advisor

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What did you get from Stirling's approximation?

Related to Evaluate Limit with Factorials: \lim_{n \to \infty}

1. What is the definition of a limit with factorials?

A limit with factorials is a mathematical concept that describes the behavior of a sequence of numbers as the input value approaches infinity. It is denoted by the notation \lim_{n \to \infty} and is used to determine the ultimate value or behavior of a sequence.

2. How does a limit with factorials differ from regular limits?

A limit with factorials takes into account the factorial function, which involves multiplying a series of descending natural numbers. This can result in different behaviors and values compared to regular limits, which only consider the behavior of the input value as it approaches a specific number.

3. What are some common techniques for evaluating limits with factorials?

Some common techniques for evaluating limits with factorials include using the ratio test, the root test, or the comparison test. These methods involve manipulating the sequence in different ways to determine its behavior and ultimately the limit value.

4. How do you know if a limit with factorials exists?

A limit with factorials exists if the sequence converges to a specific value or if the sequence approaches infinity or negative infinity. If the sequence oscillates or has no clear pattern, then the limit does not exist.

5. Can a limit with factorials be evaluated without using mathematical techniques?

In some cases, a limit with factorials can be evaluated without using mathematical techniques by recognizing patterns or simplifying the sequence. However, for more complex or undefined sequences, it is necessary to use mathematical techniques to evaluate the limit.