Provide an example of a sequence with the givenproperty. a)A sequence that has s

Question

Provide an example of a sequence with the givenproperty. a)A sequence that has subsequences that converge to 1,2, and3. b)A sequence that has subsequences that converge to and -. c)A sequence that has a strictly increasing subsequence, astrictly decreasing subsequence, and a constant subsequence. d)An unbounded sequence which has a convergentsubsequence. e)A sequence that has no convergent subsequence. Provide an example of a sequence with the givenproperty. a)A sequence that has subsequences that converge to 1,2, and3. b)A sequence that has subsequences that converge to and -. c)A sequence that has a strictly increasing subsequence, astrictly decreasing subsequence, and a constant subsequence. d)An unbounded sequence which has a convergentsubsequence. e)A sequence that has no convergent subsequence.

Explanation / Answer

Provide an example of a sequence with the givenproperty. a)A sequence that has subsequences that converge to 1,2, and3. {1,2,3,1,2,3,1,2,3,...} b)A sequence that has subsequences that converge to and -. {1,-1,2,-2,3,-3,4,-4,5,-5,...} c)A sequence that has a strictly increasing subsequence, astrictly decreasing subsequence, and a constant subsequence. {0,1,-1,0,2,-2,0,3,-3,0,4,-4,...} d)An unbounded sequence which has a convergentsubsequence. {0,1,0,2,0,3,0,4,0,5,0,6,...} e)A sequence that has no convergent subsequence. {0,1,2,3,4,...}

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