Results 1 to 2 of 2

Thread: The Integral Test

  1. #1
    Junior Member
    Joined
    Feb 2009
    Posts
    30

    The Integral Test

    Do the series diverge or converge? and why?

    1.) n=1 to infinity (5/n+1)

    2.) n=1 to infinity (-2/n(square root n))

    3.)n=2 to infinity (ln n/(square root n))

    4.)n=1 to infinity (1+ 1/n)^n

    5.)n=1 to infinity (n/n^2+1)
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    12,880
    Thanks
    1946
    Quote Originally Posted by TAG16 View Post
    Do the series diverge or converge? and why?

    1.) n=1 to infinity (5/n+1)

    2.) n=1 to infinity (-2/n(square root n))

    3.)n=2 to infinity (ln n/(square root n))

    4.)n=1 to infinity (1+ 1/n)^n

    5.)n=1 to infinity (n/n^2+1)
    1. $\displaystyle \sum_{n = 1}^{\infty}{\frac{5}{n + 1}} \geq \int_{1}^{\infty}{\frac{5}{x + 1}\,dx}$

    $\displaystyle \int_{1}^{\infty}{\frac{5}{x + 1}\,dx} = \lim_{\varepsilon \to \infty}5\ln{(\varepsilon + 1)} - \ln{(0 + 1)} \to \infty$

    This tends to $\displaystyle \infty$, and so the series, which is no less than this integral, also tends to $\displaystyle \infty$. So the series diverges.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Integral Test and comparison test help!
    Posted in the Calculus Forum
    Replies: 6
    Last Post: Jun 3rd 2009, 09:46 PM
  2. Integral Test
    Posted in the Calculus Forum
    Replies: 2
    Last Post: Mar 31st 2009, 02:54 PM
  3. Integral Test
    Posted in the Calculus Forum
    Replies: 3
    Last Post: Jan 28th 2009, 05:56 AM
  4. Integral Test/Comparison Test
    Posted in the Calculus Forum
    Replies: 1
    Last Post: Jan 27th 2009, 10:58 AM
  5. Integral Test
    Posted in the Calculus Forum
    Replies: 5
    Last Post: May 4th 2008, 08:43 AM

Search Tags


/mathhelpforum @mathhelpforum