Prove using only the definition of O that n 1025 n2 1 is

Prove using only the definition of O() that (n + 10)^2.5 + n^2 + 1 is O(n^2.5). Write your proof using proper mathematical formalism, as done in the lecture notes.

Solution

For finding out the O() of any function,first we need to eliminate all lower order terms of function

In given example,

(n+10)^2.5 +n^2 +1

After expanding and eliminating constants we can see that

n^2.5 +n^2

This are only remaining yes with n

For O(),we need highest power term

Hence,O(n^2. 5)