Calculate limit for the following function

Question

I want to calculate the limit for the following function.

$$\lim_{n\to+\infty} \frac{(3/2)^n}{(\log n)^{\log n}}$$

I have tried it using L'Hospital use but the result of differentiation is much more complicated.

score 2 · Accepted Answer · answered Sep 15 '13 at 22:38

2

Hint: $$ \frac{(3/2)^x}{(\log x)^{\log x}}=e^{x\log(1.5)-\log(x)\log\log(x)} $$

answered Sep 15 '13 at 22:38

Arash

1

pretty natural and pretty much the simplest (+1) – robjohn Sep 15 '13 at 22:40

1 Answers1