## 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_kâ‰¤ 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_kâ‰¤ 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

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