Section10.6-Power Series

Ii theseriesconvergesforallx iii

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Unformatted text preview: series converges only when x = c. ii) The series converges for all x. iii) There is a positive number, R, such that the series converges if | x – c | < R and diverges if | x – c | > R. Summarize Series Radius of convergence Interval of convergence xn R = 1 ( ‐1 , 1 ) n 0 xn n! n 0 R = ∞ ( ‐ ∞, ∞ ) n ! x 3 n 0 3 x 2 n 1 n 0 n R = 0 x = 3 n R = 1 [ 1, 3 ) Interpret The possible intervals ofconvergence for a power n series centered at c, , are: bn x c n 0 x = c (c – R, c + R] [c – R, c + R) [c – R, c + R] (c – R, c + R) (‐ ∞, ∞) TryIt.1 10n x 1 n2 n 1 n Find the radius and interval of convergence. TryIt.2 n 1 4 x 1 n n Find the radius and interval of convergence. TryIt.3 bn 10n is divergent, If is convergent and bn 8 n n 0 n 0 then what about bn 2 b 10 n n 0 n 0 bn 2 n n 0 b 8 n 0 n bn11n n 0 n n n Geometric Power Series 1 1 x x x x 1 x 2 3 n if x 1 1 1 x x...
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