Chapter 4, Problem 22R

Explanation of Solution

Given:

It is given that the ${\text{(n+1)}}^{\text{5}}\text{=}\text{O}\left({\text{n}}^{\text{5}}\right)$.

Big-Oh notation:

In big-Oh notation, let “f” and “g” be functions from the integers or the real numbers to the real numbers. It means that f(x) is “$\text{O}\left(\text{g}\left(\text{x}\right)\right)$” if there are constants “C” and “k” such that

$\left|\text{f}\left(\text{x}\right)\right|\le \text{C}\left|\text{g}\left(\text{x}\right)\right|\text{where}\text{x > k}$

Proof:

The given condition is true. Let us take the given function and it can be written as follows:

${\text{(n+1)}}^{\text{5}}\text{=}\text{c}{\text{.n}}^{\text{5}}$

• Now, compare the above expression with the definition of big-Oh