The question is calculate the values up to n=6, and guess an explicit formula where: $$n = 1, f(1) = 1\\ n = 2, f(2) = 1\\ n = 3, \frac{(f(n-1))^2 + f(n-2)}{f(n-1) + f(n-2)}$$
Anytime from 3 onwards, plugging it in, the answers will always spit out 1 as the answer. So I did it up to $f(6)$ and once again got 6. SO I have to guess an explicit formula and then use mathematical induction to prove it.
I guessed the formula to just be $f(n) = n / n$
induction: $$f(1) = 1 / 1 = 1\\ f(2) = 2 / 2 = 1\\ f(3) = 3 / 3 = 1 $$ and so on.
Is this actual mathematical induction? and if not, what would i have to do for it to be?
For induction, you start by proving some "base case." Proceed by assuming your inductive hypothesis to be true for $n$ and showing that it holds for $n+1$