Sequence and series

Sequence and series

Postby sofia123 » Wed Feb 03, 2021 6:36 am

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!
sofia123
 
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Re: sequence and series

Postby Guest » Wed Feb 03, 2021 11:04 am

sofia123 wrote: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!



sorry English is not my first language, by limited I meant bounded
Guest
 

Re: Sequence and series

Postby Guest » Mon Feb 08, 2021 1:54 am

Hey I'm trying to solve this lottery number
There is a series going on
A new number opens in lottery between 1-100

Last seven numbers were 47,99,46,70,64,64,61
If someone can solve it, tell me
Guest
 

Re: Sequence and series

Postby Guest » Thu Mar 11, 2021 12:05 pm

Guest wrote:Hey I'm trying to solve this lottery number
There is a series going on
A new number opens in lottery between 1-100

Last seven numbers were 47,99,46,70,64,64,61
If someone can solve it, tell me

First, don't "hijack" someone else's thread to ask an unrelated question! Start your own thread.

Second, what are you asking? You understand, don't you, that the whole point of a lottery is that each number is determined randomly, that there is no way to know the next number.
Guest
 


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