Results 1 to 5 of 5

Math Help - Infinite Series Problem

  1. #1
    Junior Member
    Joined
    Jan 2010
    Posts
    28

    Infinite Series Problem

    I'm sure this problem is obvious, but I don't know where to start.

    Determine whether the series converges or diverges and give a good explanation how you arrived at your conclusion.

    \Sigma^{\infty}_{n = 1}n\sin{\frac{1}{n}}

    Also, for \Sigma^{\infty}_{n = 1}\frac{1}{3 + n^2}, I know I can use the integral test to show it converges, but can I also use the comparison test, comparing it to \Sigma^{\infty}_{n = 1}\frac{1}{n^2}?

    Thanks in advance.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Math Engineering Student
    Krizalid's Avatar
    Joined
    Mar 2007
    From
    Santiago, Chile
    Posts
    3,654
    Thanks
    13
    Quote Originally Posted by mturner07 View Post
    \Sigma^{\infty}_{n = 1}n\sin{\frac{1}{n}}
    the limit of the general term doesn't go to zero, so it diverges.

    Quote Originally Posted by mturner07 View Post
    Also, for \Sigma^{\infty}_{n = 1}\frac{1}{3 + n^2}, I know I can use the integral test to show it converges, but can I also use the comparison test, comparing it to \Sigma^{\infty}_{n = 1}\frac{1}{n^2}?
    yes.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Jan 2010
    Posts
    28
    Isn't \lim_{n \to \infty}n\sin{\frac{1}{n}} = 0, since \infty *\sin{0} = 0?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    11,701
    Thanks
    454
    Quote Originally Posted by mturner07 View Post
    Isn't \lim_{n \to \infty}n\sin{\frac{1}{n}} = 0, since \infty *\sin{0} = 0?
    (\infty \cdot 0) is an indeterminate form.

    \lim_{n \to \infty} n \cdot \sin\left(\frac{1}{n}\right) = \lim_{\frac{1}{n} \to 0} \frac{\sin\left(\frac{1}{n}\right)}{\frac{1}{n}} = 1
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Junior Member
    Joined
    Jan 2010
    Posts
    28
    D'oh, thanks.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Infinite series problem?
    Posted in the Calculus Forum
    Replies: 1
    Last Post: April 18th 2011, 03:33 AM
  2. Infinite Series Problem
    Posted in the Calculus Forum
    Replies: 9
    Last Post: October 12th 2010, 01:59 AM
  3. Infinite series problem
    Posted in the Calculus Forum
    Replies: 3
    Last Post: March 2nd 2010, 08:02 AM
  4. infinite series problem with log
    Posted in the Calculus Forum
    Replies: 1
    Last Post: April 25th 2009, 01:15 PM
  5. Infinite Series Problem
    Posted in the Calculus Forum
    Replies: 6
    Last Post: April 5th 2008, 11:39 AM

Search Tags


/mathhelpforum @mathhelpforum