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Section 6: Power Series & the Ratio Test. Power Series: centered at x = a c n ’s are just coefficients which depend on n. Interval of Convergence : the set of x-values for which the series converges Radius of Convergence( R ) : the distance from the center of the interval to either endpoint.
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Power Series:centered at x = acn’s are just coefficients which depend on n
Interval of Convergence:the set of x-values for which the series convergesRadius of Convergence(R): the distance from the center of the interval to either endpoint
3 Cases: • R = 0 (series converges only at the center) • R = (series converges everywhere) • R =some positive number • |x – a| < R • (series converges when a – R < x < a + R )
Ex 1: The power series converges at x = 6 and diverges at x = 8. State whether the series converges, diverges, or cannot be determined at the x-values:-8, -6, -2, -1,0, 2, 5, 7, & 9
Ex 2: Find the radius of convergence of the two power series: a) b)
The Ratio Test:Let an be a series in which an > 0 for all n.
Ex 4: Determine the radius of convergence of the power series:
