Constructing a divergent series Please would you help me with this question? I've been thinking about it for ages but I've made very little headway, so if possible a hint would be ideal. 
Let  $\sum_{n=1}^∞{x_n}$ be a divergent series, where $x_n > 0$ for all $n$. Show that there is a divergent series  $\sum_{n=1}^∞{y_n}$ with $y_n > 0$ for all $n$, such that $(\frac{y_n}{x_n}) → 0.$
I have not been taught analysis formally, hence my lack of progress. I know to consider the series as a sequence of partial sums, and I tried to take the contrapositive of the statement but that just overcomplicated matters. I know I don't have many ideas to present but I have been trying this for days.
Thank you in advance. 

To make it even easier:
Define $(y_{n})$ as $y_{1}=\frac{x_{1}}{1}, y_{2}=y_{3}=\frac{x_{2}}{2}, y_{4}=y_{5}=y_{6}=\frac{x_{3}}{3},y_{7}=y_{8}=y_{9}=y_{10}=\frac{x_{4}}{4}\dots$ where every time $\frac{x_{n}}{n}$ $n$ is repeated $n$ times...
