# convergence – The series \$ f (x) = sum limits_ {n = 1} ^ { infty} – frac {1} {n} e ^ {- nx} cos (e ^ {- – nx}) \$ converge uniformly or punctually on \$ mathbb {R} \$?

I would say no, because for $$x <0$$, $$f (x) rightarrow infty$$ as $$n rightarrow infty$$ since $$e ^ {- nx} rightarrow infty$$ as $$n rightarrow infty$$. So the series does not even converge for $$x <0$$.

Also $$f (0) = sum limits_ {n = 1} ^ { infty} – frac {1} {n} cos (1)$$ which would seem to diverge for $$– infty$$.

Correct?