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May 27th, 2012, 03:40 AM   #1
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How can i find the boundaries of a convergent sequance? What are the conditions?
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May 27th, 2012, 12:04 PM   #2
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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.
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May 27th, 2012, 06:05 PM   #3
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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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