Problem 3. Let (27,1) be a. bounded sequence. Dene for each n E N an=inf{:1:k|k2n} bn=sup{mk|k2n} Show that the sequences (an) and (bu) are convergent. The limit of (an) is called the limit inferior of (Lien), and is denoted lim inf at\". The limit of (bu) is called the limit superior of (ml), and is denoted lim sup x\