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Very simple lim

  1. Oct 26, 2013 #1
    find the limit as n goes to infinity by using the sandwich theorem

    ## (3^n + 5^n + 7^n )^{\frac{1}{n}}##

    I notice the limit is 7 by using a different method (not the sandwich theorem)

    using the sandwich theorem I see that

    ## 7^n \leq 3^n + 5^n + 7^n ## but I can't seem to find a good upper bound. I can see that ## 2.7^n ## works but I can't explain why ## 7^n \leq 3^n + 5^n + 7^n \leq 2.7^n ##
     
  2. jcsd
  3. Oct 26, 2013 #2

    LCKurtz

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    Try using ##7^n\le 3^n + 5^n + 7^n \le 7^n+7^n+7^n##.
     
  4. Oct 26, 2013 #3

    Mark44

    Staff: Mentor

    I haven't worked the problem, but maybe this will help.
    ##3 \cdot 3^n \leq 3^n + 5^n + 7^n \leq 3 \cdot 7^n##

    ##\Rightarrow \lim_{n \to \infty} (3 \cdot 3^n)^{1/n} \leq \lim_{n \to \infty}(3^n + 5^n + 7^n)^{1/n} \leq \lim_{n \to \infty} (3 \cdot 7^n)^{1/n}##
     
  5. Oct 26, 2013 #4
    so simple, thanks

    I have another limits question (I've done the problem but would like someone to check it over as I'm new to limits). Should I start a new thread, or post it here? And is there a maximum amount of threads allowed per day?
     
  6. Oct 26, 2013 #5

    Mark44

    Staff: Mentor

    Please start a new thread...

    I'm not aware of any limit on the number of threads posted per day, but if you were to spam us with a very large number of them, that is probably a different story.
     
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