Find an example of a sequence with the given property. a)The sequence is monoton

Question

Find an example of a sequence with the given property. a)The sequence is monotone but not bounded. b)The sequence is bounded but not monotone c)The sequence is bounded and strictly increasing d)The sequence is convergent but not monotone e)The sequence is strictly decreasing but not convergent f)The sequence is neither bounded nor monotone g)The sequence is bounded below, not bounded above, andcontains an infinite number of negative terms. Find an example of a sequence with the given property. a)The sequence is monotone but not bounded. b)The sequence is bounded but not monotone c)The sequence is bounded and strictly increasing d)The sequence is convergent but not monotone e)The sequence is strictly decreasing but not convergent f)The sequence is neither bounded nor monotone g)The sequence is bounded below, not bounded above, andcontains an infinite number of negative terms.

Explanation / Answer

Answers Find an example of a sequence with the given property. a)The sequence is monotone but not bounded.    {1,2,3,...} That is {xn} where xn =n. b)The sequence is bounded but not monotone    {1,2,1,2,1,2,....} that is {xn} wherexn =1 if n is odd xn=2 if n is even c)The sequence is bounded and strictly increasing      {xn} where xn = 1 - 1/n. d)The sequence is convergent but not monotone     {xn} where xn = 1+  (-1)n /n e)The sequence is strictly decreasing but not convergent    {xn} where xn = -n. f)The sequence is neither bounded nor monotone      {xn} where xn =(-1)nn. g)The sequence is bounded below, not bounded above, and contains aninfinite number of negative terms.    {xn} where xn = n. if n is even                          = -1/n if n is odd      (If you want explanation for any of thesesequence please ask me.)

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