# subsequence example2

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.

• Think about having half of the terms be $42$ and the other half (say)... – hardmath Sep 25 '13 at 23:29
• 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... – fretty Sep 25 '13 at 23:29
• 42,0,42,0,42,0,... – fretty Sep 25 '13 at 23:30
• Well, I am trying to. – user87274 Sep 25 '13 at 23:37
• @fretty And thanks for helping me. – user87274 Sep 25 '13 at 23:37

$$a_n=\left\{\begin{array}{rcl} 5 & \mbox{if} &n \text{ is odd}, \\ 42 & \mbox{if} & n \text{ is even}. \end{array} \right.$$
• This sequence oscillates between $5$ and $42$: $a_1 =5, a_2=42, a_3=5, a_4=42, \ldots$ – Twink Sep 25 '13 at 23:45
• You don't need to have a formula. Just think of the sequence as $(5,42,5,42,...)$. – Twink Sep 25 '13 at 23:52