My Math Forum  

Go Back   My Math Forum > College Math Forum > Calculus

Calculus Calculus Math Forum


Reply
 
LinkBack Thread Tools Display Modes
November 2nd, 2011, 10:33 AM   #1
Newbie
 
Joined: Oct 2011

Posts: 8
Thanks: 0

What is the limit of

The sequence is bounded and monotone and therefore it converges. What is the limit:
PetraLenski is offline  
 
November 2nd, 2011, 02:06 PM   #2
Senior Member
 
Joined: May 2011

Posts: 501
Thanks: 6

Re: What is the limit of

This infinite product does not have a closed form value.

But, you can try to get closer and closer to what it converges to.

By changing a product to a sum often helps.

This can be done by using the log.











Just playin' around. Perhaps someone has a more elegant method.
galactus is offline  
November 2nd, 2011, 02:13 PM   #3
Newbie
 
Joined: Oct 2011

Posts: 8
Thanks: 0

Re: What is the limit of

Thanks!! So to find approximately the limit I need to take the logarithm of the product. Is there any simpler way to show that the limit is not 0?
PetraLenski is offline  
November 2nd, 2011, 02:55 PM   #4
Math Team
 
Joined: Nov 2010
From: Greece, Thessaloniki

Posts: 1,990
Thanks: 133

Math Focus: pre pre pre pre pre pre pre pre pre pre pre pre calculus
Re: What is the limit of

[color=#000000]How is it possible for this product to be equal to 0?

Let ,



in order for this product to be equal to 0, at least one term has to be zero for ,
but the sequence is strictly increasing and , so and there exists no term of the product equal to zero, hence .[/color]
ZardoZ is offline  
November 3rd, 2011, 06:56 AM   #5
Newbie
 
Joined: Oct 2011

Posts: 8
Thanks: 0

Re: What is the limit of

Quote:
How is it possible for this product to be equal to 0?
Dear ZardoZ,
What you say is true for finite products, but when the number of multipliers it is not true.
PetraLenski is offline  
November 3rd, 2011, 09:10 AM   #6
Math Team
 
Joined: Nov 2010
From: Greece, Thessaloniki

Posts: 1,990
Thanks: 133

Math Focus: pre pre pre pre pre pre pre pre pre pre pre pre calculus
Re: What is the limit of

[color=#000000]Ok then we will have to prove two theorems, which have to be answered in the complex analysis section! My proof is obvious for finite products though! I'll post them later or tomorrow.[/color]
ZardoZ is offline  
November 4th, 2011, 07:09 AM   #7
Math Team
 
Joined: Nov 2010
From: Greece, Thessaloniki

Posts: 1,990
Thanks: 133

Math Focus: pre pre pre pre pre pre pre pre pre pre pre pre calculus
Re: What is the limit of

[color=#000000]Using the second theorem which can be found here,

since

we conclude that .[/color]
ZardoZ is offline  
Reply

  My Math Forum > College Math Forum > Calculus

Tags
limit



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
limit panky Calculus 6 January 5th, 2012 04:35 PM
do this with limit superconduct Calculus 3 December 31st, 2011 10:11 AM
Limit Superior and Limit Inferior veronicak5678 Real Analysis 4 August 22nd, 2011 10:07 AM
limit (cos(1\x))|tan x| x--> .5pi rambo123 Calculus 5 December 5th, 2010 10:26 AM
when should we evaluate left limit and right limit? conjecture Calculus 1 July 24th, 2008 01:14 PM





Copyright © 2019 My Math Forum. All rights reserved.