Im struggling on a problem ive been given in class and was wondering if anyone could point me in the right direction for the solution?
The question is:
Prove that n^2>=2n+3 for n>=3
Am i correct in assuming this is proof by induction?
So would I then do n=k
so k^2>=2k+3
Then do I do n=k+1??
Proof by induction always has two parts.
Base step. Show that the statement is true for some minimal integer n. In this case, you want n = 3 because you're not interested in any integer lower than that.
So in the base step you need to show that 3^2 >= 2(3) + 3.
(Base step is usually the easy part.)
Inductive step. Here you need to show that if the statement is true for n, then it's also true for n + 1.
So you can make the assumption that for some arbitrary given integer n, it has already been shown that n^2 >= 2n + 3.
You can use this to show that it must follow that (n + 1)^2 >= 2(n + 1) + 3. I would start by simplifying the equation, then compare what you get with what you already know.