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Theorem
If {an} is bounded and monotonic then { an} is convergent.
Be cautious to not misuse this theorem. It does not state that if a sequence is not bounded and/or not monotonic that it is divergent. The sequence in that instance was not monotonic but it does converge.
Note: that we can make various variants of this theorem. If {an}is bounded above and increasing after that it converges and similarly if {an} n a is bounded below and decreasing after that it converges.
Doing the following exercise will give you and opportunity to think about this aspect of children. E1) List some illustrations of exploration by four or five-year-olds that you
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* 2^(1/2)*4^(1/8)*8^(1/16)*16^(1/32) =
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