Calculate Limit

[man111]

Calculate [tex]\lim_{n \to \infty}\frac{1}{n}.(2.5.8.11..............3n-1)^{\frac{1}{n}}[/tex]

Where . means multiplication.

[martin.nikolov]

I got [tex]\frac3e[/tex], but most likely I made a mistake.

[portokal]

I think the answer is 0, but i am not sure either

[drago]

Martin is right,
[tex]\frac{3}{e}[/tex]
Just apply Stirling approximation, but firts estimate [tex]\prod_{j=1}^{n}3j-1[/tex] with something like [tex]((3n)!)^{\frac{1}{3}}[/tex] from above and below.

[man111]

drago can you explain it how can I calculate [tex]\bf \prod_{j=1}^{n}(3j-1)[/tex]

[drago]

[tex]((3n-1)!)^{\frac{1}{3}} \lt \prod_{j=1}^{n}(3j-1) \lt ((3n+2)!)^{\frac{1}{3}}[/tex]
then use Stirling approximation.