Proving the Limit: (n+a)!/(n+b)! as n Goes to Infinity

yanjt · Aug 15, 2009

Hi,I have no idea on how to begin with this question.The question is:

Prove that (n+a)!/(n+b)! ~ n^a-b as n goes to infinity.There are clue given that we can use Euler's limit and Stirling's formula to solve this question.Can you please give me some hints on how to start with this question?

Thanks!

slider142 · Aug 15, 2009

I don't think any advanced machinery is necessary here. For any n, the term n!/n! = 1 can be ignored so we have left only a factors containing n in the numerator and b factors containing n in the denominator. You can then either note the polynomial expansion of the top and bottom, or note that a and b are constants, and thus are negligible as n increases without bound.

Proving the Limit: (n+a)!/(n+b)! as n Goes to Infinity

1. What is the limit as n goes to infinity for (n+a)!/(n+b)!?

2. How do you prove the limit of (n+a)!/(n+b)! as n goes to infinity?

3. Can the limit of (n+a)!/(n+b)! as n goes to infinity be solved algebraically?

4. What is the significance of proving the limit of (n+a)!/(n+b)! as n goes to infinity?

5. How can the limit of (n+a)!/(n+b)! as n goes to infinity be used in real-world scenarios?

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