Problem 1171 (difficulty: 5/10)

(a) For which real values of \(\displaystyle c\) will the series \(\displaystyle \displaystyle\sum_{n=1}^\infty\Big(n^c\cdot\cos(nx)\Big)\) converge on \(\displaystyle \R\)?

(b) For which real values of \(\displaystyle c\) will the series \(\displaystyle \displaystyle\sum_{n=1}^\infty\Big(n^c\cdot\sin(nx)\Big)\) converge uniformly on \(\displaystyle \R\)?

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