Fibonacci Sequence - Faster method?
"fibonnaci" is a misspelling.

There really isn't any need for jQuery here.

As you have already observed, there is also no need to keep the entire array, unless you wanted to modify the code to reuse the memoized results for multiple calculations.

If you want the fastest way to calculate a specific Fibonacci number, even when the number is large, then go for the closed-form formula instead:

$$
F_n = \frac{\phi^n - \psi^n}{\sqrt{5}}
$$
… where
\$\phi = \dfrac{1 + \sqrt{5}}{2}\$ and \$\psi = \dfrac{1 - \sqrt{5}}{2}\$.