(Solution) - Prove Theorem 7 2 20 a Show that using 7 2 19 we can write and -(2025 Original AI-Free Solution)

Paper Details

Prove Theorem 7.2.20.
a. Show that, using (7.2.19), we can write

and, since (r+1) is a maximum,
When is the inequality and equality?
b. Now use Jensen's inequality to show that
Which together with part (a) proves the theorem.