(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

[tex]a_n=(\frac{1}{n})^{\frac{1}{\ln{n}}}[/tex]

2. Relevant equations

3. The attempt at a solution

[tex]\lim_{x\rightarrow \infty}(\frac{1}{n})^{\frac{1}{\ln{n}}}[/tex]

[tex]y=(\frac{1}{n})^{\frac{1}{\ln{n}}}[/tex]

[tex]\ln{y}=\frac{\ln{\frac{1}{n}}}{\ln{n}}[/tex]

[tex]\ln{y}=\frac{\ln{1}-\ln{n}}{\ln{n}}[/tex]

[tex]\ln{y}=\frac{\ln{1}}{\ln{n}}-\frac{\ln{n}}{\ln{n}}[/tex]

[tex]\ln{y}=0-1[/tex]

[tex]e^{\ln{y}}=e^{-1}[/tex]

[tex]\lim_{x\rightarrow \infty}(\frac{1}{n})^{\frac{1}{\ln{n}}}=e^{-1}[/tex]

the back of my book says the answer is indeed [itex]e^{-1}[/itex] but im not sure if this is the way to go to for the solution or whether im supposed to rewrite it as something similar to [itex]\lim_{x\rightarrow \infty}(1+\frac{x}{n})^{n}[/itex]

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Am i doing this right?/convergence of sequences

**Physics Forums | Science Articles, Homework Help, Discussion**