1. Limited time only! Sign up for a free 30min personal 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!

Limit question with Substituting

  1. Oct 28, 2011 #1
    Fine the limit of (x^1000 - 1)/(x - 1) as x approaches 1.

    Solution:


    (x^1000 - 1)/(x - 1) = (x^999 + x^998 + ... + x + 1)(x - 1)/(x - 1)

    = (x^999 + x^998 + ... + x + 1)

    Substituting x = 1 I get....

    Line (1):1 + 11 + 12 + ..... + 1999 = 1 + 999 = 1000

    Is there any way to prove Line (1): I know it is obvious but I want to prove it mathematically and with out obviously counting it on my fingers.
     
  2. jcsd
  3. Oct 28, 2011 #2
    I guess I could say 1 + 1(999) = 1000
     
  4. Oct 28, 2011 #3
    If any one has a better way of solving it please let me know, I want to learn all I can.
     
  5. Oct 28, 2011 #4

    SammyS

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member

    You could use synthetic division.
     
  6. Oct 28, 2011 #5

    Simon Bridge

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    It's one of the surprising solutions that the limit as x --> 1 of (x^N -1)/(x-1) = N ... in the limit, the numerator is N times bigger than the denominator.

    The question is to prove the expansion - you can demonstrate it simply enough by multiplying out the brackets so it is not clear what you mean when you want a non finger-counting method.
     
  7. Oct 28, 2011 #6

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    You could use l'Hopital's theorem, if you have that.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Limit question with Substituting
  1. Substitution Question (Replies: 14)

  2. Substitution Question (Replies: 7)

  3. Substitution question (Replies: 1)

Loading...