State the premise that you are trying to prove. In algebra, induction proof always starts using letters so your premise looks like this:
n²>=2n
Verify that your premise is true for at least one case. For example, take the premise n²>=2n where n= 2,3,...
Form the induction hypothesis that you want to prove. If n²>=2n then we assume it is also true for n=k, where k=2,3,..., so k²>=2k. Therefore if it is true for n=k we must now prove it is true for n=k+1.
Prove your induction. Now you must actually prove that your premise is true. This involves actually writing the problem out and solving it. See section two for the written problem.
Conclude the problem by stating your conclusions. Algebra always requires that you make a formal statement of the proof at the end of every problem you solve. Since n²>=2n and n=k+1 then (k+1)²>=2(k+1) for every (k+1)=2,3,...
Take n=2 and solve for n.
n²>=2n
n²=4 2n=4 So 4>=4 and we know this works for n=2. Now we assume n=k for some integer k. We must prove that this works for n=k+1.
(k+1)²>=2(k+1)
k²+2k+2>=2k+2
We know k=n and n²=2n so k²=2k.
2k+2k+2>= 2k+2
We know 2k>1 because k>1(premise n=k= 2,3,...)
2k+2k+1>2k+2
The left side is greater than right side so the induction proof is solved.