Results 1 to 3 of 3

Math Help - limit questions

  1. #1
    Banned
    Joined
    Mar 2011
    Posts
    118

    limit questions

    Find the radius of convergence of the power series: ((n!)^2/(2n)!)x^n

    My answer; 0 using a(n+1)/a(n)

    Find the limits, if they exists, of
    i) 100(ln(x))/x^3 as n tends to infinity

    ii) (sinx-x)/(cosx -x^2-1) as n tends to 0

    My working i) pretty certain its infinity but not sure how to show it

    ii) no idea on this one.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Opalg's Avatar
    Joined
    Aug 2007
    From
    Leeds, UK
    Posts
    4,041
    Thanks
    7
    Quote Originally Posted by poirot View Post
    Find the radius of convergence of the power series: ((n!)^2/(2n)!)x^n

    My answer; 0 using a(n+1)/a(n)
    a(n+1) = \dfrac{((n+1)!)^2}{(2(n+1))!}. But (n+1)! = (n+1)n!, and (2(n+1))! = (2n+2)! = (2n+2)(2n+1)(2n)!. Now take another look at a(n+1)/a(n) and see if you still get the same result.

    Quote Originally Posted by poirot View Post
    Find the limits, if they exists, of
    i) 100(ln(x))/x^3 as n (x, not n, presumably?) tends to infinity

    ii) (sinx-x)/(cosx -x^2-1) as n (x again?) tends to 0

    My working i) pretty certain its infinity but not sure how to show it

    ii) no idea on this one.
    L'H˘pital's rule should do these (apply it repeatedly until you get an answer). For i), you can guess what the answer should be (and it's not infinity) if you remember the general principle that ln(x) tends to infinity more slowly than any positive power of x.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Banned
    Joined
    Mar 2011
    Posts
    118
    ok I got 0.5, 0 and non exsistent respectively. Can I use l'hopital's rule for sequences or just functions? Thank for the help.

    I am doing an analysis exam next month on limits of sequences, series and functions. I don't suppose you have any tips as I often feel like i'm stumbling in the darkness trying to figure out which method to use.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Please help with limit questions...
    Posted in the Calculus Forum
    Replies: 8
    Last Post: February 7th 2011, 07:25 PM
  2. New Limit questions
    Posted in the Pre-Calculus Forum
    Replies: 6
    Last Post: October 6th 2009, 01:22 PM
  3. Limit Law Questions
    Posted in the Calculus Forum
    Replies: 2
    Last Post: September 17th 2009, 06:19 AM
  4. limit questions
    Posted in the Calculus Forum
    Replies: 4
    Last Post: July 17th 2009, 06:40 PM
  5. 2 Limit Questions
    Posted in the Calculus Forum
    Replies: 4
    Last Post: January 19th 2009, 08:37 PM

Search Tags


/mathhelpforum @mathhelpforum