(3) (a) Determine whether the series is convergent or divergent. Explain why. n (b) Show that the function f(z) = zsin- has no limit as the complex variable z → 0. Z (Hint: Try to approach 0 along two different paths.)

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A: To examine the given sequence regarding convergence, that is study the limits as n tends to infinity

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Q: (H) The geometric series is n=1 (i) (ii) Converge Diverge

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A: We have to prove that xn has a convergent subsequence in each of the given cases.

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Q: (i) Let F(x) be a power series. Then the radius of convergence of F(x) can be negative.

A: This is a problem related to power series. Please follow the procedure given below.

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Q: ercise 3. (i) Show that 9(x) = ▶ cos(kx) Σ 3k k=1 defines a continuous function g: [0, ½] → R. (ii)…

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