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 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: 6,764 Thanks: 697 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 $\sum a_nx^n$, 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 $\left|\frac{a_{n+1}x^{n+1}}{a_nx^n}\right|= \left|\frac{a_{n+1}}{a_n}\right||x|$. 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 $\frac{a_{n+1}}{a_n}$ is 1 or -1.

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