Calc limit of a series My HW is
$$\lim\limits_{n\to\infty}\dfrac{1\cdot x+2\cdot x^2+3\cdot x^3+\dots+n\cdot x^n}{n\cdot x^{n+1}}$$ as $$x\gt1$$
I've multiplied both numerator and denominator by $$1/x^n$$
so my answer $$1/x$$ 
I was told that it is not correct.
Can anybody please help? 

$$\lim\limits_{n\to\infty}\dfrac{1\cdot x+2\cdot x^2+3\cdot x^3+\dots+n\cdot x^n}{n\cdot x^{n+1}}$$ as $$x\gt1$$
Here it is $\frac{\infty}{\infty}$, let us use L'Hôpital's rule.
If I differentiate $n$-times (the least surviving order) and then take $n->\infty $, will solve it.
$$\lim\limits_{n\to\infty}\Big(\dfrac{n\cdot n\cdot(n-1)\cdot(n-2)\dots1}{n\cdot(n+1)\cdot n\cdot(n-1)\dots 1\cdot x^{1}} = \dfrac{1}{(n+1)x} \Big) \rightarrow 0 $$
