Results 1 to 4 of 4

Math Help - Ratio Test

  1. #1
    Member
    Joined
    Apr 2008
    Posts
    132

    Ratio Test

    Use the ratio test to prove that

    converges,at least for x>0.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor Mathstud28's Avatar
    Joined
    Mar 2008
    From
    Pennsylvania
    Posts
    3,641
    Quote Originally Posted by matty888 View Post
    Use the ratio test to prove that

    converges,at least for x>0.
    \lim_{n\to\infty}\frac{x\cdot{x^{n}}}{(n+1)n!}\cdo  t\frac{n!}{x^n}\Rightarrow\lim_{n\to\infty}\frac{x  }{n+1}=0<1
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Apr 2008
    Posts
    132

    Further help plz!

    hey thanks for replying to all my questions,could you please explain how you got the first part of this?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor Mathstud28's Avatar
    Joined
    Mar 2008
    From
    Pennsylvania
    Posts
    3,641
    Quote Originally Posted by matty888 View Post
    hey thanks for replying to all my questions,could you please explain how you got the first part of this?
    Definition of ratio test is if \lim_{n\to\infty}\frac{a_{n+1}}{a_n}<1 it converges....so a_{n+1}=\frac{x^{n+1}}{(n+1)!}=\frac{x\cdot{x^{n}}  }{(n+1)n!} and divding by a_n is the same as multiplying by its reciporcal which would be \frac{n!}{x^{n}}
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Clarification of Root Test & Ratio Test
    Posted in the Calculus Forum
    Replies: 4
    Last Post: July 28th 2010, 08:45 AM
  2. Root test & Ratio test
    Posted in the Calculus Forum
    Replies: 3
    Last Post: March 14th 2010, 04:31 AM
  3. Replies: 7
    Last Post: June 4th 2009, 10:33 PM
  4. Huh? Ratio test contradicts root test?
    Posted in the Calculus Forum
    Replies: 4
    Last Post: March 25th 2009, 01:07 PM
  5. ratio test (series) urgent test tommorow!
    Posted in the Calculus Forum
    Replies: 3
    Last Post: December 2nd 2008, 04:27 PM

Search Tags


/mathhelpforum @mathhelpforum