Consider the following power series: f x = 1...

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MAC2312 Spring 2015 Quiz 13 Name: Please show all appropriate work on the back of this of this quiz or on attached pages. For all work, please indicate the question number clearly and circle your answer. You have 25 minutes to complete this quiz. 1. Consider the following power series: f ( x ) = 1 + 2 2 · 1 x + 4 3 · 2 · 1 x 2 + 8 4 · 3 · 2 · 1 x 3 + · · · (a) Write a formula for the sequence of coefficients: c n = 2 n - 1 n ! (b) Write the power series in summation notation, including the index:
(c) Using your summation expression, find the radius of convergence:
(d) Using your summation expression, find the interval of convergence:
2. Express the function

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