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Limit WITHOUT using l'hospital

  1. Jan 21, 2009 #1
    For [tex]p,q\in \mathbb{N}[/tex], determine [tex]\lim_{x\to1} \frac{x^{p}-1}{x^{q}-1}[/tex]

    I know that it should be p/q. Without using L'hospitals rule, how do I determine it?
  2. jcsd
  3. Jan 21, 2009 #2
    The quotient can be rewritten as (1-xp )/(1-xq ). Since x is less than 1 try a binomial expansion.
  4. Jan 21, 2009 #3
    Factoring :)
  5. Jan 21, 2009 #4
    Got it! My methods of trying were way more complicated. Don't know why I didn't think of that at first!

    (x^n) - 1=(x-1)(x^(n-1) + ... + x + 1)

    Thanks NoMoreExams
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