10.2-part1-solutions

# 10.2-part1-solutions - MthSc 108 Learning Activity...

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MthSc 108 – Learning Activity Solutions 10.2 : Power Series Part 1 PART I Do not use a calculator! State the name of the test you use and the specific criteria for that test which allows you to make the determination about convergence of the power series. Give a concluding statement in a complete (non-mathematical) written sentence. For each power series: a. State the center. b. Write out the first three terms. c. Determine the radius of convergence. d. Find the interval of convergence. 1. (2 x + 3) n n n = 1 a. (2 x + 3) n n n = 1 is a power series centered at x = - 3 2 . b. (2 x + 3) n n n = 1 = (2 x + 3) + (2 x + 3) 2 2 + (2 x + 3) 3 3 + ... c. For a n = (2 x + 3) n n and a n + 1 = (2 x + 3) n + 1 n + 1 consider lim n →∞ a n + 1 a n : lim n →∞ (2 x + 3) n + 1 n (2 x + 3) n ( n + 1) = lim n →∞ (2 x + 3) n n + 1 = 2 x + 3 lim n →∞ n n + 1 = 2 x + 3 . By the Ratio Test, the power series converges absolutely if

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10.2-part1-solutions - MthSc 108 Learning Activity...

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