Definition of a limit - problem 3

: Math 2730 Sequences and Series: Definition of a limit - problem 3
   By Martin Daniels on Thursday, January 17, 2008 - 09:58 pm: Edit Post

I've been working on the definiton of a limit problems that are posted on the webpage.

Most i found to be fairly straight forward, but i forget how to tackle the problem when the variable is embedded in a natural log function as in question 3:

A(n)= 1 / ln(n+1)

I can get the situation where 1/E < ln(n+1) but then i am stuck. I want to use the exponential function to "kill" the natural log for some reason...

   By Sasho on Friday, January 18, 2008 - 08:34 am: Edit Post

Good. Now apply the function e^{x} to both sides of the last inequality; that is, raise e to both the left and the right hand side of the last inequality. Get: e^{1/E}<e^{ln(n+1)}; then use the fact that lnx and e^{x} are mutual inverses, so that e^{lnz}=z for every z (in the domain of ln).

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