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Intervals of Convergence Problem

Intervals of Convergence Problem - GROUP WORK 3 SECTION...

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Unformatted text preview: GROUP WORK 3, SECTION l2.8 Intervals of Convergence . . 0° x" I. Consrder the power series 2 . "=1 [’1 (a) Find the radius of convergence. (b) Find expressions for the two series at the endpoints of the interval of convergence. (c) Determine whether the series in part (b) converge. (d) What is the interval of convergence? DO 2. Consider the power series 2 nnx“. ”:1 (a) Write each term of the series in the form (b,,)”. What is b"? (b) Let x be any fixed positive number. What can we say about b" and (bn)” as n —> oo? 00 (c) What does part (b) tell us about the convergence or divergence of Z n”x"? ”:1 CO ((1) Compute the radius and interval of convergence of Z n"x”. Hz] 6789 ...
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