Showing a series is some range

Question

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!

What is the base of this logarithm, is it $e$ or $10$ or... ? By the way this is not quite a series, it is a finite sum. — peter.petrov, Apr 21 '20 at 11:39

score 0 · Answer 1 · answered Apr 21 '20 at 11:38

0

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.

answered Apr 21 '20 at 11:38

peter.petrov

I tried that before and used the sterling approximation but thats apparently wrong because they are looking for upper and lower bound – Delta Hex Apr 21 '20 at 13:05

1 Answers1