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1 10 5 Power Series Definition A power series is Goal Given a power series determine the values of x for which the series is convergent Known as the interval of convergence Result Examples Find the interval of convergence for X xn n 0 1 When finding the interval of convergence of a power series there are 3 possible results 1 X n 0 2 X n 0 3 X n 0 cn x a n converges only when cn x a n converges for cn x a n converges on Definition The radius of convergence of a power series Find the radius and interval of convergence of X n xn n 0 2 X Find the radius and interval of convergence of x2n 1 2n 1 n 0 Find the radius and interval of convergence of X x 2 n n 1 6n n 0 3
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