Where did the cosines come from?

Calculus Level 2

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

True or false?:

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

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

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