Find the limit.

Question

Find the limit.

zenmo · Answer

$$\lim_{n \rightarrow \infty}\left| \frac{ (3n+1)(3n)(3n-1) }{ (n+1)^3 } \right|$$

zenmo · Answer

Do I use L'hopital rule on this, since it looks like oo/oo ?

zepdrix · Answer

Hmm, no.
You should be able to do this one just by eyeballing it.

Largest term in the numerator would be 27n^3, right?
How bout the bottom? n^3 ya?

zenmo · Answer

Ah, the largest term. Got it now, thanks

mathmale · Answer

Your function is an absolute value.  However, you can take the "lim" inside the absolute value symbols and apply it to (3n+1)(3n)(3n-1)/(n+1)^3.

I agree with zepdrix, however, that there are easier ways of doing this problem.  Hint:  Determine the highest-powered term of each the numerator and the denominator.

Ignoring all the other terms, take the limit as n approaches infinity of your result.