Chapter 3.4, Problem 18ES

Some of the arguments in 7-18 are valid by universal modus ponens or universal modus tollens; other are invalid and exhibit the converse or the inverse error. State which are valid and which are invalid. Justify your answers.
If an infinite series converges, then the terms go to 0.

The terms of the infinite series ${\displaystyle \underset{n-1}{\overset{n}{\sum }}\frac{1}{n+1}}$ do not go to 0.

$\therefore$ The infinite series ${\displaystyle \underset{n-1}{\overset{n}{\sum }}\frac{1}{n+1}}$ do not converges.