The 'Rigging' Method

Hi, i am a little confused with this method.
I am supposed to 'rig' on this divergence.
Prove that lim n-> infinity e^n + n! + ln n = infinity

e^n +n! + ln n > k , e^n +ln n > k , e^n > k , n > ln k

I have no idea is this is correct. I am supposed to be making the LHS smaller for a divergence question though.