Results 1 to 2 of 2

Math Help - series - converge or diverge

  1. #1
    Junior Member
    Joined
    Mar 2008
    Posts
    45

    series - converge or diverge

    Hi all,

    I am trying to determine if the following series converges or diverges:

    <br />
\sum_{n=1}^{\infty}\frac{sin^2(n)}{n^2}<br />

    Not sure if what i did is correct:

    -1 <= sin(n) <= 1

    1 <= sin^2(n) <= 1

    1/n^2 <= [sin^2(n)]/ n^2 <= 1/n^2

    Note: sin^2(n) = [sin(n)]^2

    I then compared the series to 1/n^2 and determined that the series 1/n^2 is a harmonic p series, where p > 1 and so it converges. Thus, the series <br />
\sum_{n=1}^{\infty}\frac{sin^2(n)}{n^2}<br />
converges.

    Could someone tell me if i am doing this correctly

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

  2. #2
    MHF Contributor

    Joined
    Apr 2005
    Posts
    15,298
    Thanks
    1276
    Quote Originally Posted by ArTiCK View Post
    Hi all,

    I am trying to determine if the following series converges or diverges:

    <br />
\sum_{n=1}^{\infty}\frac{sin^2(n)}{n^2}<br />

    Not sure if what i did is correct:

    -1 <= sin(n) <= 1

    1 <= sin^2(n) <= 1
    You mean -1<= sin^2(n)<= 1 but the comparison test uses absolute values that doesn't matter.

    1/n^2 <= [sin^2(n)]/ n^2 <= 1/n^2

    Note: sin^2(n) = [sin(n)]^2

    I then compared the series to 1/n^2 and determined that the series 1/n^2 is a harmonic p series, where p > 1 and so it converges. Thus, the series <br />
\sum_{n=1}^{\infty}\frac{sin^2(n)}{n^2}<br />
converges.

    Could someone tell me if i am doing this correctly

    Thanks in advance,
    ArTiCk
    Except for the unimportant sign error, yes.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. [SOLVED] Series - Converge or diverge
    Posted in the Calculus Forum
    Replies: 4
    Last Post: August 6th 2010, 01:25 PM
  2. series converge or diverge?
    Posted in the Calculus Forum
    Replies: 1
    Last Post: April 15th 2010, 06:37 PM
  3. Series Converge or diverge 2
    Posted in the Calculus Forum
    Replies: 1
    Last Post: November 23rd 2008, 06:18 PM
  4. Series help!; converge or diverge
    Posted in the Calculus Forum
    Replies: 2
    Last Post: November 23rd 2008, 05:19 PM
  5. More on series converge or diverge?
    Posted in the Calculus Forum
    Replies: 2
    Last Post: May 21st 2008, 02:28 AM

Search Tags


/mathhelpforum @mathhelpforum