Results 1 to 2 of 2

Math Help - show that lim(a^n+b^n)^(1/n) = b if 0<a<b

  1. #1
    Junior Member
    Joined
    May 2007
    Posts
    34

    show that lim(a^n+b^n)^(1/n) = b if 0<a<b

    lim(a^n+b^n)^(1/n) = b if 0<a<b

    i don't even know what to say. lost.

    *edit*

    ok got an idea: i know that (a^n+b^n)^(1/n) < (b^n+b^n)^(1/n) = 2^(1/n)*b, which converges to b

    i'm thinking of using the squeeze theorem, i just need to find a lower bound that converges to b..

    *edit*

    found it: (b^n)^(1/n) < (a^n+b^n)^(1/n)

    sorry for spamming... i gotta remember the motto: everything you need is in the problem.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    Joined
    Aug 2009
    From
    Israel
    Posts
    976
    (a^n+b^n)^{\frac{1}{n}} = b(\frac{a^n}{b^n} + 1)^{\frac{1}{n}}

    but \lim_{n\to +\infty} \frac{a^n}{b^n} = 0 since b>a.

    \Rightarrow \lim_{n \to +\infty} b(\frac{a^n}{b^n}+1)^{\frac{1}{n}} = b(1)^{\frac{1}{n}} = b
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Using the MVT to show this
    Posted in the Calculus Forum
    Replies: 0
    Last Post: November 25th 2010, 11:19 AM
  2. Show the sum
    Posted in the Calculus Forum
    Replies: 5
    Last Post: October 21st 2010, 03:28 AM
  3. Show that f o g is one-to-one
    Posted in the Calculus Forum
    Replies: 2
    Last Post: January 24th 2010, 06:29 PM
  4. Show that ln5 < 1 + 1/2 + 1/3 + 1/4.
    Posted in the Calculus Forum
    Replies: 2
    Last Post: April 6th 2009, 01:29 AM
  5. how to show show this proof using MAX
    Posted in the Calculus Forum
    Replies: 2
    Last Post: January 14th 2009, 12:05 PM

Search Tags


/mathhelpforum @mathhelpforum