I want to show that $$ a_n = \frac{3^n}{n!} $$ converges to zero. I tried Stirlings formulae, by it the fraction becomes $$ \frac{3^n}{\sqrt{2\pi n} (n^n/e^n)} $$ which equals $$ \frac{1}{\sqrt{2\pi n}} \left( \frac{3e}{n} \right)^n $$ from this can I conclude that it goes to zero because $\frac{3e}{n}$ and $\frac{1}{\sqrt{2\pi n}}$ approaching zero?
Subscribe to:
Post Comments (Atom)
-
So if I have a matrix and I put it into RREF and keep track of the row operations, I can then write it as a product of elementary matrices. ...
-
I am asked to prove the density of irrationals in $\mathbb{R}$. I understand how to do this by proving the density of $\mathbb{Q}$ first, na...
-
Can someone just explain to me the basic process of what is going on here? I understand everything until we start adding 1's then after ...
No comments:
Post a Comment