I'm slightly confused about some sort of "proof" (probably not a real proof since it's physics math) I have the formula
$f(x) = f(y) + (x-y)f'(y) + \frac{f''(y)}{2\epsilon}, \quad \epsilon \in (x,y)$
f(x) = -x lnx rewritten in the formula becomes $f(x) = -x \ln y -x+y - \frac{1}{2\epsilon}$
Which somehow can be used to prove that the Shannon entropy $S(\vec{p}) = -\sum_i^n p_i \ln p_i \leq \ln n$ And I can't simply see how I will do it. Someone who know which obvious step I'm missing or if the professor simply has done some writing error? (wouldn't be the fist time)
Your professor used $y=1/n$. Can you take it from here?