May 27th, 2012, 03:40 AM  #1 
Senior Member Joined: Apr 2012 Posts: 135 Thanks: 1  boundaries
How can i find the boundaries of a convergent sequance? What are the conditions? 
May 27th, 2012, 12:04 PM  #2 
Global Moderator Joined: May 2007 Posts: 6,704 Thanks: 670  Re: boundaries
Are you asking about a series or a sequence? Is there a variable involved? Usually you would use a ratio test in some form, but you need to more specific about what you have in mind. An example would help.

May 27th, 2012, 06:05 PM  #3 
Math Team Joined: Sep 2007 Posts: 2,409 Thanks: 6  Re: boundaries
As mathman said, a "sequence" or "series" does not have a "boundary". I think that you are talking about a "power series" or series of the form , which always has an "interval of convergence". The simplest thing to do to find the interval of convergence for a power series is, again as mathman said, to use the ratio test. Look at . The series will converge where the limit of that, as n goes to infinity, is less than 1, diverge where it is greater than 1. The "boundary" points, or endpoints, of the interval of convergence will be where the limit of the fraction is 1 or 1.


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