• Support PF! Buy your school textbooks, materials and every day products Here!

Limits of factorials

  • Thread starter dlf387
  • Start date
  • #1
5
0

Homework Statement


Find the lim as n-->inf of the sequence
{an}=
1x3x5x...x(2n-1)
_______________
n!


Homework Equations





The Attempt at a Solution


I rewrote it as
...(2n-3)(2n-2)(2n-1)
__________________
n(n-1)(n-2)...2x1
which leads me to belive that is converges at infinity--is this at all correct

Homework Statement





Homework Equations





The Attempt at a Solution

 
Last edited by a moderator:

Answers and Replies

  • #2
HallsofIvy
Science Advisor
Homework Helper
41,833
955

Homework Statement


Find the lim as n-->inf of the sequence
{an}=
1x3x5x...x(2n-1)
_______________
n!


Homework Equations





The Attempt at a Solution


I rewrote it as
...(2n-3)(2n-2)(2n-1)
__________________
n(n-1)(n-2)...2x1
which leads me to belive that is converges at infinity--is this at all correct?
No, that's not correct. And I don't know why you would say that leads you to believe it converges. Obviously, the the denominator cancels with part of the numerator:
[tex]\frac{(2n-1)!}{n!}= (n+1)(n+2)\cdot\cdot\cdot(2n-1)[/tex]

That does not converge.

Homework Statement





Homework Equations





The Attempt at a Solution

 
  • #3
5
0
Thank you for your reply but I have not had much experience with factorials. Could you please fill in the steps to reach how you got to that final expression? Also, could you please help me understand how to get a finite limit from a factorial?
thanks
 
  • #4
Dick
Science Advisor
Homework Helper
26,258
618
No, that's not correct. And I don't know why you would say that leads you to believe it converges. Obviously, the the denominator cancels with part of the numerator:
[tex]\frac{(2n-1)!}{n!}= (n+1)(n+2)\cdot\cdot\cdot(2n-1)[/tex]

That does not converge.
I think the question is actually about (2n-1)!!/n!. I.e. for n=5, (1*3*5*7*9)/(1*2*3*4*5). If you write that as (1/1)*(3/2)*(5/3)*(7/4)*(9/5) you can see that all of the factors are greater than 1. In fact, a lot of them are greater than 1.5. If n is large what does this tell you about the product?
 
  • #5
5
0
Thank you very much for the reply. When you write it out like that I can see that the product will eventually reach infinity. But how did you know to rewrite the expression as (2n-1)!!/n!
and what does a double factorial mean?
thanks
 
  • #6
5
0
Thank you very much for the reply. When you write it out like that I can see that the product will eventually reach infinity. But how did you know to rewrite the expression as (2n-1)!!/n!
and what does a double factorial mean?
thanks
 
  • #7
Dick
Science Advisor
Homework Helper
26,258
618
Thank you very much for the reply. When you write it out like that I can see that the product will eventually reach infinity. But how did you know to rewrite the expression as (2n-1)!!/n!
and what does a double factorial mean?
thanks
You can look up 'double factorial' on line. It's just a shorthand way of writing your product, 1*3*5*7*9=9!!.
 
  • #8
5
0
I am sorry to belabor the point, but is there anyway to reduce (2n-1)!!/n!
to a more simpler form--like the 1st commentator did? is what they did correct?

i think that n! can be written as (1x2x(n-1)x(n-2)x...x(n)) but could that cancel with anything from the numerator?
thanks
 
  • #9
Dick
Science Advisor
Homework Helper
26,258
618
Not really. The 2n-1 in the numerator doesn't cancel with anything in the denominator and the even numbers in the denominator don't cancel with anything in the numerator.
 

Related Threads on Limits of factorials

  • Last Post
Replies
1
Views
2K
  • Last Post
Replies
7
Views
11K
  • Last Post
Replies
4
Views
15K
  • Last Post
Replies
5
Views
4K
  • Last Post
Replies
10
Views
3K
  • Last Post
Replies
4
Views
3K
  • Last Post
Replies
6
Views
1K
  • Last Post
Replies
4
Views
1K
  • Last Post
Replies
1
Views
2K
  • Last Post
Replies
11
Views
2K
Top