Question: (a) Give a proof of Weierstrass M-test. (b) Derive Theorem 4 from Theorem 3. (c) Prove that uniform convergence of a series in a region
(a) Give a proof of Weierstrass M-test.
(b) Derive Theorem 4 from Theorem 3.
(c) Prove that uniform convergence of a series in a region G implies uniform convergence in any portion of G. Is the converse true?
(d) Find the precise region of convergence of the series in Example 2 with x replaced by a complex variable z.
(e) Show that x2 Σˆžm=1 (1 + x2)-m = 1 if x ‰ 0 and 0 if x = 0. Verify by computation that the partial sums s1, s2, s3 look as shown in Fig. 369
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a Convergence follows from the comparison test Sec 151 Let R n z and R n be the remain... View full answer
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