(Solved): Problem 3. 1. Let an+1=an2 with a1=31 what is limnan ? 2. Let an+1=si ...

Expert Answer

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To find the limit of the sequence    with    as n approaches infinity, we can observe the pattern of the sequence.
  , and so on.

We can see that as    increases, the terms of the sequence    approach 0.

Therefore, the limit of the sequence as    approaches infinity is   .

2. To show that the sequence    with    converges to 0 as n approaches infinity, we need to demonstrate two properties:

(i) The sequence is bounded. (ii) The sequence is monotonic.