Q$1).($a$)$ State if each of the following mathematical statements are TRUE or FALSE. Provide a brief justification for your answer.

$($i$)$ The Harmonic series converges to $\frac{1}{n}.$

$(2$ marks$)$

$($ii$)$ The sequence $\{(-1{)}^{n+1}{\}}_n=1^{}$ is bounded.

$(2$ marks$)$

$($iii$)$ The sequence $\{r^n{\}}_n=1^{}$ converges for all

$(2$ marks$)$