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.
by
Paulo Guilherme Santos