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 
$$\lim_{x\to 0}\sum_{n=1}^\infty \frac x n$$ 

If you mean $\displaystyle \lim_{x\to0} \left( x \sum_{n=1}^\infty \frac 1 n \right),$ then that is $\lim\limits_{x\to0} (x\cdot\infty) = \lim\limits_{x\to0} \infty = \infty. $
But if you mean $\displaystyle \left( \lim_{x\to0} x \right) \sum_{n=1}^\infty \frac 1 n,$ then that is $0\cdot\infty,$ which in some contexts one should interpret as $0.$
However, remember also that if two expressions $A$ and $B$ both vary as functions of $x$ and $\lim\limits_{x\to0} A = 0$ and $\lim\limits_{x\to0} B = \infty,$ then $\lim\limits_{x\to0} (AB)$ may be some particular number, such as (for example) $8,$ depending on which functions $A$ and $B$ are.
