Hello I am having some issues trying to show the following series is in the range between 60 and 150
I have to use a non-integral method to show the following.
$60 \leq \sum_{n=1}^{32} \lg(k) \leq 150 $
Also I am not allowed to actually evaluate the summation.
I am just lost as to how to actually approach this problem, not sure if I should use some kind of proof method or not.
Thank you!
Use that
$\lg(a) + \lg(b) = \lg(ab)$
Thus the sum becomes $\lg (32!)$
Then I guess you need to make a few "smart" observations to obtain these bounds.