By using the fact that $\log(n)<

Question

By using the fact that $\log(n)<<n$，evaluate $$\lim_{n\to \infty} n^{1/n}$$

How to use $\log(n)<<n$ to evaluate that?

Please see https://math.meta.stackexchange.com/questions/5020/ — Angina Seng, Nov 01 '18 at 09:05
What have you already tried? If you can add your workings and thoughts to the question you'll get more appropriate answers. — MRobinson, Nov 01 '18 at 09:08

score 3 · Accepted Answer · answered Nov 01 '18 at 09:05

3

HINT

Use that

$$\large {(\log n)^\frac1n = e^{\frac{\log n}n}}$$

answered Nov 01 '18 at 09:05

user

thank you,i got it. – miny Nov 01 '18 at 09:33
1

@miny Well done! You are welcome. That's a standard trick for the manipulation of expressions like $f(x)^{g(x)}$ in calculus with $f(x)>0$. Keep that in mind! Bye – user Nov 01 '18 at 09:36

1 Answers1