Thread: Small doubt

Hi

Does the sequence defined by (-1)^n diverge or oscillate? I know technically it oscillates but in my MCQ options there are 4 options in which oscillation is not given.

the options are:
1. diverges
2. converges
3. absolutely converges
4. none of these

therefore, would the answer be none of these or "Diverges" ?

P.S: is oscilllation a sub-set of diverging ? (something like if oscillation is happening then it must diverge? )

Originally Posted by champrock

Hi

Does the sequence defined by (-1)^n diverge or oscillate? I know technically it oscillates but in my MCQ options there are 4 options in which oscillation is not given.

the options are:
1. diverges
2. converges
3. absolutely converges
4. none of these

therefore, would the answer be none of these or "Diverges" ?

P.S: is oscilllation a sub-set of diverging ? (something like if oscillation is happening then it must diverge? )

I would say "diverge" ... a sequence that does not converge to a fixed limit diverges.