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In the textbook, there is a question about whether or not a sequence that does not converge to 42 and yet have infinitely many terms of the sequence equal to 42.

I am having a hard time coming up with examples of such sequences, and so need some hints to help me think clearly.

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  • $\begingroup$ Think about having half of the terms be $42$ and the other half (say)... $\endgroup$ – hardmath Sep 25 '13 at 23:29
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    $\begingroup$ Can you not think for yourself? You have asked three simple questions about sequences in the past half an hour and have yet to acknowledge the answers given to you... $\endgroup$ – fretty Sep 25 '13 at 23:29
  • $\begingroup$ 42,0,42,0,42,0,... $\endgroup$ – fretty Sep 25 '13 at 23:30
  • $\begingroup$ Well, I am trying to. $\endgroup$ – user87274 Sep 25 '13 at 23:37
  • $\begingroup$ @fretty And thanks for helping me. $\endgroup$ – user87274 Sep 25 '13 at 23:37
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Let

$$a_n=\left\{\begin{array}{rcl} 5 & \mbox{if} &n \text{ is odd}, \\ 42 & \mbox{if} & n \text{ is even}. \end{array} \right.$$

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  • $\begingroup$ Could you please give an explanation of your example? I don't get it. $\endgroup$ – user87274 Sep 25 '13 at 23:42
  • $\begingroup$ This sequence oscillates between $5$ and $42$: $a_1 =5, a_2=42, a_3=5, a_4=42, \ldots$ $\endgroup$ – Twink Sep 25 '13 at 23:45
  • $\begingroup$ Wow. I don't have any idea on how to come up with it's formula. $\endgroup$ – user87274 Sep 25 '13 at 23:48
  • $\begingroup$ You don't need to have a formula. Just think of the sequence as $(5,42,5,42,...)$. $\endgroup$ – Twink Sep 25 '13 at 23:52
  • $\begingroup$ Well, for me the formula actually makes more sense that a sequence itself. $\endgroup$ – user87274 Sep 25 '13 at 23:54

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