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Unformatted text preview:  xa  < R (i.e. take everything that’s not  xa  to the other side, this includes constants). You’ve found R ! 2 How to ﬁnd the interval of convergence I 1. Find R ﬁrst, i.e. the equation  xa  < R . 2. Expand the inequality. 3. Test the series at the endpoints to see if the series converges there. Examples Find the radius and interval of convergence of the following series. 1. ∞ X n =0 1 n + 1 ( x4) n 3 2. ∞ X n =0 ( x2) n 10 n 3. ∞ X n =0 3 n x n n ! 4 4. ∞ X n =0 n !( x + 2) n In summary, there are 3 possibilities when ﬁnding R : 1. ∑ converges only when x = a . 2. ∑ converges for all x . 3. There is an R > 0 such that ∑ converges if  xa  < R and diverges if  xa  > R . 5...
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This note was uploaded on 03/03/2010 for the course MATH 2224 taught by Professor Mecothren during the Spring '03 term at Virginia Tech.
 Spring '03
 MECothren
 Multivariable Calculus, Power Series

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