5. (6 marks) use mathematical induction to prove that for each integer n ≥ 4, 5^n ≥ 2^2n+1 + 100.
( take +100 into considersation since previous solution didnt )

Step-by-step explanation:

We will prove by mathematical induction that, for every natural ,  

We will prove our base case, when n=4, to be true.

Base case:

Inductive hypothesis:  

Given a natural ,  

Now, we will assume the induction hypothesis and then use this assumption, involving n, to prove the statement for n + 1.

Inductive step:

With this we have proved our statement to be true for n+1.  

In conlusion, for every natural .

36 is the final answer! : )