Chapter 4, Problem 38C

Explanation of Solution

Given:

It is given that ${\displaystyle \sum _{i=1}^n{i}^2}=O\left(n^3\right)$.

Proof:

Let us prove the above statement by defining the sum by an integral. Consider the following assumption:

  ${\displaystyle \sum _{i=1}^n{i}^2}={\displaystyle \underset{0}{\overset{n+}{\int }}}$