# Thread: Direct Comparison Test Question

1. ## Direct Comparison Test Question

LIMIT COMPARISON TEST (sorry)

1/[2(square of n) + (cube root of n)] compared with 1/(square of n)

I understand how to do the problem, my question is: how do I know to choose that equation to compare it with when there are two different n's in the denominator (n^1/2) and (n^3/2).

2. Originally Posted by jujab
LIMIT COMPARISON TEST (sorry)

1/[2(square of n) + (cube root of n)] compared with 1/(square of n)

I understand how to do the problem, my question is: how do I know to choose that equation to compare it with when there are two different n's in the denominator (n^1/2) and (n^3/2).
What exactly is the problem?

$\displaystyle \frac{1}{2n^2+\sqrt[3]{n}}$ compared with $\displaystyle \frac{1}{n^2}$

Or did you mean to say "square root of n", in which case it's

$\displaystyle \frac{1}{2\sqrt{n}+\sqrt[3]{n}}$ compared with $\displaystyle \frac{1}{\sqrt{n}}$

3. I meant square root of n, thanks for catching that!