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: 
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. 
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?

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] 
November 3rd, 2011, 06:56 AM  #5  
Newbie Joined: Oct 2011 Posts: 8 Thanks: 0  Re: What is the limit of Quote:
What you say is true for finite products, but when the number of multipliers it is not true.  
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] 
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 

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