1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

How do i find the limit to this fraction (n=>infinity)

  1. Nov 12, 2008 #1
    [(n+5)/(n-1)]^n

    i get [infinity/nifinity]^infinity and i dont see anything to change
     
  2. jcsd
  3. Nov 12, 2008 #2

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    A little bit more accurately, as n goes to infinity (n+5)/(n+1) goes to 1 so this is of the form [itex]1^{\infty}= 1[/itex].

    If this weren't in the "precalculus" section, I would recommend using L'Hopital's rule!
     
  4. Nov 12, 2008 #3

    Mark44

    Staff: Mentor

    True enough that it's of the indeterminate form [tex]1^\infty[/tex], but it's not necessarily equal to 1. Another limit with this form is lim (1 + 1/n)^n, for n approaching [tex]\infty[/tex]. The limit here is the natural number, e.
     
  5. Nov 12, 2008 #4
    all true, but the limits anwer is e^6
     
  6. Nov 12, 2008 #5

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    !

    Yes! Mark44 essentially gives that! Dividing, (n+5)/(n-1)= 1+ 6/(n-1) so ((n+5)/(n-1))n= (1+ 6/(n-1))n. Since, for n going to infinity, the difference between n and n-1 is negligible, the limit is the same as the limit of (1+ 6/n)n= (1+ (6/n))6(n/6)= (1+ 1/m)6m where m= 6/n. That is [(1+ 1/m)m]6. As Mark44 said, the limit of (1+ 1/m)m is e so the limit of [(1+ 1/m)m]6 is e6

    His response was far more helpful than mine was!
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: How do i find the limit to this fraction (n=>infinity)
Loading...