Phys 208 – Theoretical Physics – Test 1 ( Sept. 29, 2004)1. (20 pts)Find the interval of convergence for the following power series; be sure toinvestigate the endpoints of the interval.()−=∞∑122321nnnxn2. (20 pts)Recall the binomial series is, !()!111212323+=++−+− −+xpxppxpxp"where pis any real number, positive or negative.Find the Maclaurin series for the function defined by the following integral. . Hint: Multiply (or divide) the sine series by anfxttdtxsin=−∫120appropriate series and integrate the first three terms.3. (20 pts.)Find the roots of . You can leave the roots in polar form.−164i4. (20 pts)Evaluate in Cartesian form, .21ii+
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