# pointwise convergence

Am I right in saying that the sequence of functions $$f_n(x)=\displaystyle\frac{xn^\alpha}{e^{nx}\times\ln(n)}$$ converges pointwise to 0 $\forall{x}\in\mathbb{R}$?

Thanks for any help

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You are right for $x \ge 0$. –  André Nicolas Oct 27 '11 at 23:27

No, take $x=-1$ then you get $\displaystyle \frac{-e^n n^{\alpha}}{\log(n)}\to-\infty$
Yes, for $x\geqslant 0$ this is true since $\displaystyle \frac{1}{e^{xn}}$ dominates the rest of the terms. –  Alex Youcis Oct 27 '11 at 23:28