$4$

PROBLEM SHEET $1$

Problem $4.[20$ pts$]($a$)$ State the Bounded Monotone sequence theorem.

$($b$)$ Use the Bounded Monotone sequence to prove the following sequence is conve gent and find the limit:

$\underset{n}{lim}{x}_n=\underset{n}{lim}(2-\frac{3}{n})=$dots

$($c$)$ State the Bolzano$-$Weierstrass theorem.