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Complicated Limit from Analysis

  • Thread starter nickmai123
  • Start date
  • #1
78
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I need some help showing the following limit. I don't really know where to start, and I was just looking for a quick tip or two to begin the proof. Thanks!

Problem:

[tex]\lim_{n\rightarrow\infty} \sqrt[n]{\alpha^n+\beta^n} = max (\alpha,\beta)[/tex]
 

Answers and Replies

  • #2
10
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1. From symmetry, you can assume that alpha >= beta.
2. Now you need to prove that the limit is alpha.
3. Remember the trick where you multiply and then divide by same factor (Think, what factor should it be?).
 

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