i was wondering how to evaluate $\lim\limits_{x \to0} x\sum 1/n$ I was wondering how to evaluate 
$$\lim_{x\to 0}x\sum_{n=1}^\infty \frac 1 n$$ 
Edit
so that it's clear I mean 
$$\lim_{x\to 0}x*\sum_{n=1}^\infty \frac 1 n$$ 
witch is equvalent to 
$$\lim_{x\to 0}\sum_{n=1}^\infty \frac x n$$ 

$$\lim_{x\to 0}x\sum_{n=1}^\infty\frac1n=\left(\sum_{n=1}^\infty\frac1n\right)\lim_{x\to 0}x$$
since the series does not depend on $x$. Hence, the above expression is undefined, as 
$$\sum_{n=1}^\infty\frac1n$$
is divergent.
