Where did the cosines come from?

Calculus Level 2

Let \( \sum\limits_{n=0}^\infty a_n \) and \( \sum\limits_{n=0}^\infty b_n \) be two convergent numerical series with positive terms.

True or false?:

The series \( \sum\limits_{n=0}^\infty \left(a_n\cos(b_nx)+b_n\sin(a_nx) \right) \) is convergent in \(\mathbb{R} \).

These problem is from a test by Professor Maria do Ceú.
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