# Homework_4.pdf - Homework-4 Q1 Find the sum of the series...

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Homework-4 Q1 Find the sum of the series X n =0 n 2 2 n by first finding the sum of the power series, X n =0 n 2 x n = x + 4 x 2 + 9 x 3 + 16 x 4 + ... Hint: Use the geometric series, 1 1 - x = X n =0 x n , x ( - 1 , 1) . Q2 If f ( x ) = X n =0 c n x n , where c n +4 = c n for all n 0, find the interval of convergence of the series and a formula for f ( x ). Q3 If k is a positive integer, find the radius of convergence of the series X n =0 ( n !) k ( kn )! x n . Q4 Suppose that you know that the series X n =0 b n x n converges when | x | < 2 . What can you say about the following series? Why? X n =0 b n n + 1 x n +1 Q5 Find a value for a constant k that will make the radius of convergence of the power series

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