I am not able to solve this exercise. I've tried everything.
Exercise Let be $a_n > 0$ a sequence and suppose that $\sum a_n$ converges. Prove that exists a sequence $c_n > 0$ such that $\lim c_n = \infty$ and $\sum c_na_n < \infty$
I don't even know if I have to find an "always-valid" closed form for $c_n$ (maybe in function of $a_n$?) or prove its existence in another way.
Thanks in advance.