Infinite Sequence Involving A Factorial

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Homework Help Overview

The discussion revolves around the sequence defined by a_n = (2n - 1)! / (2n)^n, focusing on its behavior as n approaches infinity.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants express uncertainty regarding the steps needed to analyze the sequence, questioning whether to find its limit or sum it. There is also a request for clarification on any missing information relevant to the problem.

Discussion Status

Some participants have provided hints suggesting the exploration of bounds for the sequence, indicating a potential direction for analysis without reaching a consensus on the approach.

Contextual Notes

One participant noted the need to take the limit as n approaches infinity, while others are still clarifying the requirements of the problem.

Bashyboy
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Homework Statement


[itex]a_n = \frac{(2n -1)!}{(2n)^n}[/itex]


Homework Equations





The Attempt at a Solution


I am not exactly sure how to solve this problem.
 
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Bashyboy said:

Homework Statement


[itex]a_n = \frac{(2n -1)!}{(2n)^n}[/itex]


Homework Equations





The Attempt at a Solution


I am not exactly sure how to solve this problem.


What are you supposed to do with an? Find its limit? Sum it?

RGV
 
Oh, I am sorry that I did not specify. I need to take the limit as n goes to infinity of this sequence.
 
Does it seem, to anyone, that I have left any more information out?
 
Hint: Try looking at a bound...what's it greater than, or what's it less than. Then take the limit of that, you should have your answer.
 

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