I have tried investigate the convergence/divergence of the following question, yet ended up with having it converging when it's supposed to converge:
an = (-1)^n . (n+2)/(3n-1)
Stacey Warren - Expert brainly.com
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Yeah, it will diverge. Although the limit as n approaches infinity has that (n+2)/(3n-1) approaches 1/3, the (-1)^n multiplier will have your limit oscillate...it won't be able to converge.
so because (-1)^n diverges, by the theorem if one diverges all will diverge and therefore the sequence will diverge?
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Kind of...in order for a sequence to converge, it must head toward a single value - that's the motivation for the definition. As you have that (-1)^n thing attached, you won't have the case where you approach one value...you essentially approach two values: -1/3 and +1/3.