Course Solutions Uncategorized (Solved) : 1 Give Example Divergent Sequence Im Converges B Give Example Divergent Sequences Bn Abn C Q32768743 . . . .

(Solved) : 1 Give Example Divergent Sequence Im Converges B Give Example Divergent Sequences Bn Abn C Q32768743 . . . .

 

(1) (a) Give an example of a divergent sequence [an^ such that im an converges (b) Give an example of divergent sequences an and bn such that abn) converges. (2) Consider the sequence (a) Show that an < 2 for all n Hint: Clearly ai < 2. Show: if an < 2 then an+ < 2. This is enough to show that an < 2 for all n; formally speaking, this is a proof by induction (b) Sho that {any is increasing by proving the inequality an > an-I Hint: use an-V2an-1 and the fact that 2 >an1 (c) 

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