Hi,
I'm trying to solve this exercise can you help me?
Consider the sequence an= [tex](-1)^{n-1}\frac{2^{n}+n}{3^{n}-\sqrt{n}}[/tex], say and justify whether it’s true or false that:
1)an is limited
2)the series Σan is absolutely convergent
3)A={an: |an| < = 1/100} doesn't have a maximum
4)for each n in n sup(an) > 0
what I though
2)V I can say that the series has the same behavior of [tex]\frac{2^{n}}{3^{n}}[/tex] and use the root test.
1)V since the series converge then the sequence an converge so it has to be limited
3)F I draw it and it didn’t make sense but I don’t have any proper justification
4)V same thing as the third
can you tell me if my answer are correct and how can I justify them? Thanks!