Section10.6-Power Series

X 3 1 x 3 2 x 3 3 x 3 n 2 3 n 0

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Unformatted text preview: ! x 3 n 2 3 n 0 Find the radius and interval of convergence: an 1 n 1 ! x 3 n an n! x 3 n 1 n 1 x 3 lim n an 1 an unless | x – 3 | = 0 Interval of convergence: x = 3 Radius of convergence, R = 0 Example 3 x 2 n 1 n 0 n Find the interval and radius of convergence: an 1 an 3 x2 n n2 3 x2 n 1 3 x2 x2 lim n 1 n n 1 3 x2 n 1 n2 n 1 n2 an 1 x2 an n Example ‐ continued lim n an 1 x2 an Convergent for | x – 2 | < 1 Divergent for | x – 2 | > 1 What about | x – 2 | = 1 ? Ratio Test is inconclusive. Use another test. Example – continued 3 x 2 n 1 n 0 n x 2 1 3 1 n 1 n 0 n Convergent Checking | x – 2 | = 1 x 2 1 3 n 1 n0 Divergent Series is convergent for ‐1 ≤ x – 2 < 1 ; 1 ≤ x < 3 Interval of convergence: [ 1, 3 ) Radius of convergence, R = 1 Theorem bn x c n For a given power series, , there are n 0 only three possibilities: i) The...
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This note was uploaded on 02/24/2014 for the course APMA 1110 taught by Professor Morris during the Fall '11 term at UVA.

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