Give an example of an unbounded sequence that does not diverge to positive infinity or to negative infinity.

Expert Answers

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Let `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.

 

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