1. Let an be a POSITIVE infinite series (i.e. an> 0 for all n ≥ 1). Let f be a continuous function n=1 with domain R. Is each of these statements true or false? If it is true, prove it. If it is false, prove it by providing a counterexample and justify that is satisfies the required conditions.

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Q: For what Values Of X IS tne wing geommetric series convergent? 1++ 27 1) x>0 2) -1<x<1 3) -3<x<3 4)…

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Q: Ean converges and an > 0 for all n , can anything be said about E? An

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Q: 8 1. Let an be a POSITIVE infinite series (i.e. an> 0 for all n ≥ 1). Let f be a continuous function…

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Q: Find the interval of convergence and the radius of convergence for each series.

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Q: Theorem 1.5. Consider the absolutely convergent series S(x) = ao + a1x + a2x2 + ...+ akx* + ·..,…

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Q: on whernn 0o then det ermine this series E2 an is Convergent or Divergent n=2 -3 b. En=2 n2+n n2-10…

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Q: Suppose that an (x – 2)" converges for x = 8. As a consequence, which of the following statements…

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Q: 3. Prove that the series 1 x2n n! 1 + x²n n=0 converges uniformly on R to a continuously…

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Q: 1. Prove that the series E(-1)" n converges uniformly in any closed and bounded interval a, b, but…

A: 1st we prove the uniform convergence part