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Statement 1: There exists a sequence of functions g_non [0,1] so that fn is discontinuous on [0,1] forall n belongs to the set of natural numbers andg_n is uniforml...

Question

Statement 1: There exists a sequence of functions g_non [0,1] so that fn is discontinuous on [0,1] forall n belongs to the set of natural numbers andg_n is uniformly Cauchy.Statement 2: Suppose x_k is a convergence series of realnumbers and y_k≤ x_k for all k belongs to the set of naturalnumbers. Then y_k converges.Determine the above statements true or false, givecounterexample if false

Statement 1: There exists a sequence of functions g_n on [0,1] so that fn is discontinuous on [0,1] for all n belongs to the set of natural numbers and g_n is uniformly Cauchy. Statement 2: Suppose x_k is a convergence series of real numbers and y_k≤ x_k for all k belongs to the set of natural numbers. Then y_k converges. Determine the above statements true or false, give counterexample if false



Answers

Determine whether the statement is true or false. Explain your answer. If $\sum u_{k}$ converges to $L,$ then $\sum\left(1 / u_{k}\right)$ converges to $1 / L$

Okay. In this case, the statement of the exercise is true because if we can see this, they're the Syria A NBN. We take the absolute value that give us the syriza again that we know we converges via poultices, therefore, that Siri's converges absolutely. And therefore it also converges as an automated Siri's no, like the night, a series that's a serious that has positive and negative tops.


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