![Give an example of an unbounded sequence that does not diverge to positive infinity or to
negative infinity.
Solution
et [s_n=n] if [n] is even and 0 if [n] is odd, so the sequence is
0,2,0,4,0,6,...
This is unbounded but doesn't diverge to infinity or negative infinity because there will always
be values for which [s_n=0] no matter how large [n] is.](https://image.slidesharecdn.com/giveanexampleofanunboundedsequencethatdoesnotdivergetopo-230402131631-999b1781/85/Give-an-example-of-an-unbounded-sequence-that-does-not-diverge-to-po-pdf-1-320.jpg)
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Unbounded Sequence Example Not Diverging to Infinity or Negative Infinity
- 1. Give an example of an unbounded sequence that does not diverge to positive infinity or to negative infinity. Solution et [s_n=n] if [n] is even and 0 if [n] is odd, so the sequence is 0,2,0,4,0,6,... This is unbounded but doesn't diverge to infinity or negative infinity because there will always be values for which [s_n=0] no matter how large [n] is.