Results 1 to 2 of 2

Math Help - Sequences Questions (2)

  1. #1
    Junior Member
    Joined
    Sep 2009
    Posts
    27

    Sequences Questions (2)

    Two questions for y'all; both involve determining convergence or divergence, if convergence finding limit:

    1) a(sub n) = SQRT((n+1)/(9n+1)): I see that you can make that (N+1)^1/2 divided by (9n + 1)^1/2, but can't progress.

    2) a(sub n) = ((-1)^n*n^3)/(n^3+2n^2+1): Since there is the -1^n term, is this simply divergent? Or am I looking at it the wrong way?

    Cheers!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Behold, the power of SARDINES!
    TheEmptySet's Avatar
    Joined
    Feb 2008
    From
    Yuma, AZ, USA
    Posts
    3,764
    Thanks
    78
    Quote Originally Posted by Sprintz View Post
    Two questions for y'all; both involve determining convergence or divergence, if convergence finding limit:

    1) a(sub n) = SQRT((n+1)/(9n+1)): I see that you can make that (N+1)^1/2 divided by (9n + 1)^1/2, but can't progress.

    2) a(sub n) = ((-1)^n*n^3)/(n^3+2n^2+1): Since there is the -1^n term, is this simply divergent? Or am I looking at it the wrong way?

    Cheers!

    1) a_n=\sqrt{\frac{n+1}{9n+1}}

    First lets factor out the highest power of n from both the numerator and denominator to get

    a_n=\sqrt{\frac{n(1+\frac{1}{n})}{n(9+\frac{1}{n})  }}

    and reduce to get

    a_n=\sqrt{\frac{(1+\frac{1}{n})}{(9+\frac{1}{n})}}

    Now as n \to \infty \frac{1}{n} \to 0 so we get

    a_n=\sqrt{\frac{(1+0)}{(9+0)}}=\frac{1}{3}

    Your are correct that the 2nd sequence diverges, but try an analysis similar to the one I just did. Good luck.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. some questions on convergence of sequences
    Posted in the Calculus Forum
    Replies: 3
    Last Post: January 11th 2012, 04:33 PM
  2. 2 more questions about sequences..
    Posted in the Calculus Forum
    Replies: 3
    Last Post: November 29th 2011, 08:34 AM
  3. Sequences and series questions
    Posted in the Algebra Forum
    Replies: 1
    Last Post: October 25th 2010, 10:47 AM
  4. Series/Sequences Questions
    Posted in the Calculus Forum
    Replies: 3
    Last Post: March 2nd 2010, 08:24 PM
  5. Two questions about sequences
    Posted in the Differential Geometry Forum
    Replies: 0
    Last Post: October 18th 2009, 04:33 AM

Search Tags


/mathhelpforum @mathhelpforum