Taking Limit to infinity when variable is exponent? Example. I am testing $-1/4$ and $1/4$ for
$$\lim_{n \to  \infty} \frac{(-1)^n 4^n x^n}{\sqrt{n}}$$
What happens in the numerator that it makes it equal 1?
Like what happens to each term that it everything ends up as 1? 
Any help would be greatly super appreciated! Thanks

For $x = -1/4$, you have
$$\lim_{n \to \infty} \frac{(-1)^n 4^n (-1/4)^n}{\sqrt{n}}.$$
Since you have a bunch of terms all raised to the same power in the numerator, we can simplify the equation a bit by pulling these terms together inside one pair of parenthesis:
$$\lim_{n \to \infty} \frac{\big[(-1)(4)(-1/4)\big]^n}{\sqrt{n}} = \lim_{n \to \infty} \frac{1}{\sqrt{n}}.$$
I skipped a few steps I thought were obvious. I encourage you try working everything out for $x = 1/4.$
