Direct Comparison Test - Another Example 5

[nancybautista]

OMG!!! You're very straight forward and clear in explaining the concept of the comparison test. You just open my mind! What kind of an alien are you?? Lol

[jeremiahleyba]

it's pi/4<arctan(n)<pi/2 because our values start at 1, but it really doesn't affect the problem just being a OCD. lol great videos!

[tonykong]

why does it have to be greater than or equal to 0?

[leylasolmaz]

you are the best. I got A- from calculus 1 thanks to you BRO!!

[vjm]

I thought that when you multiply or divide both sides of an inequality, it flips the inequality.

So in this case:
tan^-1 (n) < (Pi/2)  (note: It's greater than or equal to)
becomes
[tan^-1 (n)] / [n^3]  > [(Pi/2) / (n^3)]  (note: Greater than or equal to)

Or am I thinking of something else?

EDIT:

I am a dumbass. The above would be correct IF and ONLY IF you multiply or divide with a NEGATIVE number. The way it's done here is correct. My bad.