Results 1 to 6 of 6

Math Help - Can Someone help me take this limit?

  1. #1
    Newbie
    Joined
    Feb 2010
    Posts
    8

    Can Someone help me take this limit?

    I know that the limit as n goes to infinity of ((n-2)/n)^n=e^-2 but I do not know the steps to arrive there. Can someone help me?
    Also how do you enter math so that it actually looks like math and not the "gobbelty gook" above
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Banned
    Joined
    Oct 2009
    Posts
    4,261
    Thanks
    2
    Quote Originally Posted by Slyprince View Post
    I know that the limit as n goes to infinity of ((n-2)/n)^n=e^-2 but I do not know the steps to arrive there. Can someone help me?
    Also how do you enter math so that it actually looks like math and not the "gobbelty gook" above


    Do you already know that \lim_{n\to\infty}\left(1+\frac{1}{f(n)}\right)^{f(  n)}=e for any function f(n)\,\,\,s.t.\,\,\, f(n)\xrightarrow [n\to\infty]{} \pm\infty ? If you do then:

    \left(\frac{n-2}{n}\right)^n=\left[\left(1+\frac{1}{-n\slash 2}\right)^{-n\slash 2}\right]^{-2}\xrightarrow [n\to\infty]{}e^{-2}

    Tonio
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor
    Joined
    Apr 2008
    Posts
    1,092
    You need to learn how to use LaTeX. There is a subforum on this website for learning how to use it.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor

    Joined
    Apr 2005
    Posts
    16,453
    Thanks
    1868
    Quote Originally Posted by Slyprince View Post
    I know that the limit as n goes to infinity of ((n-2)/n)^n=e^-2 but I do not know the steps to arrive there. Can someone help me?
    Also how do you enter math so that it actually looks like math and not the "gobbelty gook" above
    To answer your second question, use "LaTex" by staring with "[math ]" and ending with "[/math ]" without the last space.
    For example, \lim_{n\to\infty}\left(\frac{n- 2}{n}\right)^n.
    Click on that to see the code. There is also a "LaTex tutorial" on this forum.

    To answer your first question, rewrite the formula as \left(1- \frac{2}{n}\right)^n and let m= \frac{n}{2} so n= 2m. Now it becomes \left(1- \frac{1}{m}\right)^{2m} = \left[\left(1- \frac{1}{m}\right)^m\right]^2.

    Before continuing, I would need to know- what definition of "e" are you using?

    Once again, Tonio got in just ahead of me!
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Feb 2010
    Posts
    8
    Quote Originally Posted by HallsofIvy View Post
    To answer your second question, use "LaTex" by staring with "[math ]" and ending with "[/math ]" without the last space.
    For example, \lim_{n\to\infty}\left(\frac{n- 2}{n}\right)^n.
    Click on that to see the code. There is also a "LaTex tutorial" on this forum.

    To answer your first question, rewrite the formula as \left(1- \frac{2}{n}\right)^n and let m= \frac{n}{2} so n= 2m. Now it becomes \left(1- \frac{1}{m}\right)^{2m} = \left[\left(1- \frac{1}{m}\right)^m\right]^2.

    Before continuing, I would need to know- what definition of "e" are you using?

    Once again, Tonio got in just ahead of me!
    where e= the limit of (1+1/n) as n goes to infinity.
    Thanks Tonio but it seems like you went through a few steps which I did not follow. Can someone fill in the gaps. I'm in the second calculus in college (series and multivariable calculus) and I just recently learned that that was the definition of e. I was never taught that so now I'm lost when it comes to these kind of limits.

    Do you guys get paid for this. This seems a little too convenient. I was recently online and I tried to get tutored for math online and the fee was outrageous (something like $30 a month) and then I recently stumbled on this website. I guess what I'm trying to say is do you guys do this out of the goodness in your heart or do you get compensated?
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Banned
    Joined
    Oct 2009
    Posts
    4,261
    Thanks
    2
    Quote Originally Posted by Slyprince View Post
    where e= the limit of (1+1/n) as n goes to infinity.
    Thanks Tonio but it seems like you went through a few steps which I did not follow. Can someone fill in the gaps. I'm in the second calculus in college (series and multivariable calculus) and I just recently learned that that was the definition of e. I was never taught that so now I'm lost when it comes to these kind of limits.

    Do you guys get paid for this. This seems a little too convenient. I was recently online and I tried to get tutored for math online and the fee was outrageous (something like $30 a month) and then I recently stumbled on this website. I guess what I'm trying to say is do you guys do this out of the goodness in your heart or do you get compensated?

    $30 USA devaluate dollars...A MONTH...looked to you "outrageous"?? Oh, dear: you better don't learn my HOUR fee...

    Tonio
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 1
    Last Post: August 8th 2010, 12:29 PM
  2. Replies: 1
    Last Post: February 5th 2010, 04:33 AM
  3. Replies: 16
    Last Post: November 15th 2009, 05:18 PM
  4. Limit, Limit Superior, and Limit Inferior of a function
    Posted in the Differential Geometry Forum
    Replies: 2
    Last Post: September 3rd 2009, 06:05 PM
  5. Replies: 15
    Last Post: November 4th 2007, 08:21 PM

Search Tags


/mathhelpforum @mathhelpforum