Results 1 to 15 of 15

Math Help - another series...is my answer right?

  1. #1
    Member akhayoon's Avatar
    Joined
    Dec 2007
    From
    T.O
    Posts
    106

    another series...is my answer right?

    \sum(-1)^{n}[1-nsin(1/n)] determine if A.convergent, C.convergent or divergent

    I chose C.Convergent

    I saw that nsin(1/n) goes to 1 because of some other question I solved earlier and that would make everything 0

    which means that a_k \rightarrow 0 making the series conditionally convergent?

    if this is wrong, could you please point out what my error of thinking about this is? from what you see how I analyzed this atleast...

    thanks
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor Mathstud28's Avatar
    Joined
    Mar 2008
    From
    Pennsylvania
    Posts
    3,641
    Quote Originally Posted by akhayoon View Post
    \sum(-1)^{n}[1-nsin(1/n)] determine if A.convergent, C.convergent or divergent

    I chose C.Convergent

    I saw that nsin(1/n) goes to 1 because of some other question I solved earlier and that would make everything 0

    which means that a_k \rightarrow 0 making the series conditionally convergent?

    if this is wrong, could you please point out what my error of thinking about this is? from what you see how I analyzed this atleast...

    thanks
    this is wrong...is this statement true here a_{n+1}<a_n,\forall{n}\in\mathbb{Z^{+}}?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member akhayoon's Avatar
    Joined
    Dec 2007
    From
    T.O
    Posts
    106
    I don't even know what that means.....is this relevant to solving the question?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor Mathstud28's Avatar
    Joined
    Mar 2008
    From
    Pennsylvania
    Posts
    3,641
    Quote Originally Posted by akhayoon View Post
    I don't even know what that means.....is this relevant to solving the question?
    Yes...it means for every positive integer is the next term in the sequence less than the one before it...that is necesarry in proving an alternating series convergent
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Member akhayoon's Avatar
    Joined
    Dec 2007
    From
    T.O
    Posts
    106
    how would i go about doing that with something that has something like nsin(1/n) in it?
    Follow Math Help Forum on Facebook and Google+

  6. #6
    MHF Contributor Mathstud28's Avatar
    Joined
    Mar 2008
    From
    Pennsylvania
    Posts
    3,641
    Quote Originally Posted by akhayoon View Post
    how would i go about doing that with something that has something like nsin(1/n) in it?
    you evaluate it...check it...does any value of sin(1/x)<0?
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Member akhayoon's Avatar
    Joined
    Dec 2007
    From
    T.O
    Posts
    106
    I guess not, but I still can't make the connection, and I'm getting I'm getting kind of confused actually...
    Follow Math Help Forum on Facebook and Google+

  8. #8
    MHF Contributor Mathstud28's Avatar
    Joined
    Mar 2008
    From
    Pennsylvania
    Posts
    3,641
    Quote Originally Posted by akhayoon View Post
    I guess not, but I still can't make the connection, and I'm getting I'm getting kind of confused actually...
    Ok before we continue...do you actually know how to apply the alternating series test?
    Follow Math Help Forum on Facebook and Google+

  9. #9
    Member akhayoon's Avatar
    Joined
    Dec 2007
    From
    T.O
    Posts
    106
    all I know is that the series must be positive and that it must be decreasing, my main problem is I don't know how to actually apply this to a series with sin, ln etc...
    Follow Math Help Forum on Facebook and Google+

  10. #10
    MHF Contributor Mathstud28's Avatar
    Joined
    Mar 2008
    From
    Pennsylvania
    Posts
    3,641
    Quote Originally Posted by akhayoon View Post
    all I know is that the series must be positive and that it must be decreasing, my main problem is I don't know how to actually apply this to a series with sin, ln etc...
    Ok...the theorem states that if a_{n+1}<a_n and \lim_{n \to {\infty}}a_n=0...now do both those things apply to your series? If so it is conditonally convergent
    Follow Math Help Forum on Facebook and Google+

  11. #11
    Member akhayoon's Avatar
    Joined
    Dec 2007
    From
    T.O
    Posts
    106
    well I found out before that a_k goes to 0

    however, how do I show that

    (-1)^{n+1}[1-(n+1)sin(1/n+1)]< (-1)^{n}[1-nsin(1/n)]

    do I just plug in 1 for the value of n or something...in this course I can't use a calculator...
    Follow Math Help Forum on Facebook and Google+

  12. #12
    MHF Contributor Mathstud28's Avatar
    Joined
    Mar 2008
    From
    Pennsylvania
    Posts
    3,641
    Quote Originally Posted by akhayoon View Post
    well I found out before that a_k goes to 0

    however, how do I show that

    (-1)^{n+1}[1-(n+1)sin(1/n+1)]< (-1)^{n}[1-nsin(1/n)]

    do I just plug in 1 for the value of n or something...in this course I can't use a calculator...
    First of all you dont include the (-1)^{n} in the test for the decreasing terms...and I will tell you that it does decrease...so now that we know both those things what can we conclude?
    Follow Math Help Forum on Facebook and Google+

  13. #13
    Member akhayoon's Avatar
    Joined
    Dec 2007
    From
    T.O
    Posts
    106
    it must mean that it is conditionally convergent
    Follow Math Help Forum on Facebook and Google+

  14. #14
    Member akhayoon's Avatar
    Joined
    Dec 2007
    From
    T.O
    Posts
    106
    P.S if this shows up on the exams I will say that MathStud28 told me that it was decreasing and I will refer them to the link of this post lol
    Follow Math Help Forum on Facebook and Google+

  15. #15
    MHF Contributor Mathstud28's Avatar
    Joined
    Mar 2008
    From
    Pennsylvania
    Posts
    3,641
    Quote Originally Posted by akhayoon View Post
    P.S if this shows up on the exams I will say that MathStud28 told me that it was decreasing and I will refer them to the link of this post lol
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Series. AP GP. Need help with answer. Question also.
    Posted in the Pre-Calculus Forum
    Replies: 5
    Last Post: February 5th 2011, 04:29 AM
  2. Replies: 1
    Last Post: October 4th 2010, 04:46 PM
  3. Replies: 1
    Last Post: June 1st 2010, 03:17 AM
  4. Taylor Series (check my answer plz)
    Posted in the Calculus Forum
    Replies: 1
    Last Post: November 16th 2009, 01:08 AM
  5. Geometric series answer checking
    Posted in the Calculus Forum
    Replies: 1
    Last Post: August 19th 2009, 02:09 PM

Search Tags


/mathhelpforum @mathhelpforum