Question

\[\lim_{n\to\infty}\frac{\prod_{k=1}^{n}(2k-1)}{n!}\]Infinity (does not exist), right? Just need to check.

Answer 1

Similarly:\[\lim_{n\to\infty}\frac{\prod_{k=1}^{n}(2k-1)}{(2n)^n}=0\]Right? Checking again.

Answer 2

Yes, according to wolfram. What kind of class is this for, anyway? I've never formally learned how to handle these sorts of limits. @chasingblocks

Answer 3

@chasingblocks

The following commentary regarding your posted problem is from @PhoneAFriend:

"Looks like the products of odd naturals up to (2n-1) divided by n!, so I agree with the answer, but it is surprising. First glance made me think the denom. was larger and that the limit would be 0. I agree with DNE b/c there is no upper bound.

Answer 4

@Directrix

Thanks. I had to check. I have an analytical solution, but I couldn't tell if it was right because my intuition is pretty bad. It's always good to have a second opinion.

Answer 5

You are welcome.