Quote:
Originally Posted by brownkenny
I've been working through Tenenbaum's book "Introduction to Analytic and Probabilistic Number Theory" and I'm stuck on the proof of an upper bound for .
For reference, it's Theorem 3 on page 11. The desired upper bound is
Using the bound
it's easy to show that for we have
Tenenbaum then gives the bound
So far, so good. At this point in the proof, Tenenbaum says "The stated result follows by choosing " and leaves the details to the reader. As much as I've looked at it, I still can't figure out how he arrives at the desired result. Any tips/suggestions? Thanks in advance.

After the substitution factor out n/log(n) and then use partial fractions....?
This shouldn't be too bad.