(a) Consider the power series in which the coefficients a n 1, 2, 3, 1, 2, 3, 1, are periodic of period p 3 Find the radius of convergence and the sum of this power series (b) Consider a power series in which the coefficients are periodic, (a n p a p ), and a n 0 Find the radius of convergence and the sum of this power series ax 1 2x 3x2 x 2x4 3x5 x n 0

Question: (a) Consider the power series in which the coefficients a n = 1, 2, 3, 1, 2, 3, 1, . . . are periodic of

(a) Consider the power series ax" = 1 + 2x + 3x2 + x + 2x4 + in which the coefficients a_n = 1, 2, 3, 1, 2, 3, 1, . . . are periodic of period p = 3. Find the radius of convergence and the sum of this power series.(b) Consider a power series

3x5 + x + n=0

in which the coefficients are periodic, (a_n+p = a_p), and a_n > 0. Find the radius of convergence and the sum of this power series.

ax" = 1 + 2x + 3x2 + x + 2x4 + 3x5 + x + n=0

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a To find the radius of convergence of the power series with periodic coefficients we can use the ratio test The ratio test states that if the limit o... View full answer

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