Use mathematical induction to prove that for each integer n ≥ 4, 5^n ≥ 2^2n+1 + 100. (it is 5 to power of n and 2 to the power of 2n+1)

Step-by-step explanation:

The statement to be proved using mathematical induction is:

We will begin the proof showing that the base case is satisfied (n=4).

.

Then, 1 is true for n=4.

Now we will assume that the statement holds for some arbitrary natural number and prove that then, the statement holds for n+1. Observe that

With this the inductive step has been proven and then, our statement is true,

For every ,

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step-by-step explanation: