Answer
Invalid by converse error.
Work Step by Step
Converse Error: $\forall x$ if $P(x)$ then $Q(x)$.
$Q(a)$ for a particular $a$.
$\therefore P(a)$. (invalid conclusion)
In this case P(x) is: an infinite series x converges.
Q(x) is: the terms of the infinite series x go to 0.
a is the infinite series $\sum_{n=1}^{\infty} \frac{1}{n}$.
