Chapter 4, Problem 52C

Explanation of Solution

Given:

It is given that ${\displaystyle \sum _{i=1}^n\log i}=O\left(n\log n\right)$.

Proof:

Let us prove the above statement by defining the sum by the following assumption:

  $\begin{array}{c}{\displaystyle \sum _{i=1}^n\log i}\le {\displaystyle \sum _{i=1}^n}\end{array}$