# Simple limit question

1. Apr 12, 2005

### bomba923

How do I show that $$\mathop {\lim }\limits_{n \to \infty } \left( {n!!} \right)^{\left( {n^{ - n} } \right)} = 1$$ ?

(The n^-n forces the value to decrease faster than n!! increases, I believe. But how to work out that?)

Last edited: Apr 12, 2005
2. Apr 12, 2005

### estalniath

1)Firstly we'll let the expression (n!!)^(n^-n)=y, then taking ln on both sides give,
lny=ln(n!!)/n^n.
2) We'll then find the limit of the expression at the RHS using Le Hopital's rule or by observation that n^n increases faster than ln(n!!). =)
3) After finding the limit, L, all we have to do is substitute back the value of y, which is e^L

Last edited: Apr 12, 2005