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Math Help - show this series converge uniformly to a continuous function

  1. #1
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    show this series converge uniformly to a continuous function

     f(x)=\sum_{n\geq1}{a_{n}\cos(nx)}+\sum_{n\geq1}{b_  {n}\sin(nx)}\ \ \ \ \ \ with \ \ \ |a_{n}|\leq \frac{c}{n^{1+\epsilon}}, \ \ \ |a_{n}|\leq \frac{c}{n^{1+\epsilon}}
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  2. #2
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    Quote Originally Posted by silversand View Post
     f(x)=\sum_{n\geq1}{a_{n}\cos(nx)}+\sum_{n\geq1}{b_  {n}\sin(nx)}\ \ \ \ \ \ with \ \ \ |a_{n}|\leq \frac{c}{n^{1+\epsilon}}, \ \ \ |a_{n}|\leq \frac{c}{n^{1+\epsilon}}
    Use the Weierstrass M-test for the uniform convergence; and the theorem that a uniform limit of continuous functions is continuous for the continuity of f(x).
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