Question

Let {hn(x)} be a sequence of functions on R that converges to 0 uniformly. Prove that The sequence of functions f,(x) = sin (x + h„(x)) is uniformly convergent. \text

{ The series of functions } \sum_{n=1}^{\infty} \frac{\cos h_{n}(x)}{n} \text { is not convergent at any point. }

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