Limit of absolute value Fourier coefficient

$f$ continuous in $R$ with period $2\pi$ and

$f(t) = \sum_{k=- \infty }^{\infty} c_{k} e^{ikt}$

where $c_{k}$ is the complex Fourier coefficient of $f$ then

$\lim_{k \rightarrow \infty} |c_{k}|=0$

Is this true or false? If it's true can someone point me in the right direction on how to proof it? If it's false can someone give a counter example?