Q1.

a) Use mathematical induction to prove that log₂n n for all integers n 1.

b) , (theta, omega, and big O) notations are also used for functions defined on the set of non-negative integers (ie, sequences).

Use the result in part (a) to show that: 3n + log₂n is (n). I want someone to show me how to prove that 3n + log₂n is equal to big (n).

I have already answered part a), and will upload my working after this post. Please only show me working for part b)

I realise that in order to find big O notation of (n) I have to first find the big omega notation, and then the big O notation, but I am struggling to get n by itself.

Please show me a way to find b), please do not rush your answer, I have posted this question several times now, and no one has been able to provide an answer.

https://www.chegg.com/homework-help/Discrete-Mathematics-with-Applications-4th-edition-chapter-11.4-problem-47E-solution-9781133168669

This is a link to part a) of this question.

You will have to be familiar with this definitions to answer this question O-, ?-, and ?-Notations.

Thank you for your help