Answer
Valid by universal modus tollens.
Work Step by Step
Universal modus tollens: $\forall x, $ if $P(x)$ then $Q(x)$.
~$Q(a)$ for a particular $a$.
~$\therefore P(a)$.
In this case P(x) is: the infinite series x converges.
Q(x) is: the terms of the infinite series x go to 0.
a is $\sum_{n=1}^{\infty}\frac{n}{n+1}$.
