Q:

Sum of Divergent and Convergent Series

$\sum_{n=1}^{\infty}x_n$ is a convergent series and $\sum_{n=1}^{\infty}y_n$ is a divergent series. Prove their sum diverges.
My attempt:
Suppose $\sum_{n=1}^{\infty}x_n + y_n$ converges.
Since $\sum_{n=1}^{\infty}-x_n = -\sum_{n=1}^{\infty}x_n$ converges,  $\sum_{n=1}^{\infty}x_n + y_n - \sum_{n=1}^{\infty}x_n = \sum_{n=1}^{\infty}y_n$
This implies that $\sum_{n=1}^{\infty}y_n$ converges, which is a contradiction. Therefore $\sum_{n=1}^{\infty}x_n + y_n$ diverges.
How is this proof?

A:

Yes, that would be the standard way of doing it. 

