Work Step by Step
Proofs using mathematical induction consists of two steps: 1) The base case: here we prove that the statement holds for the first natural number. 2) The inductive step: assume the statement is true for some arbitrary natural number $n$ larger than the first natural number, then we prove that then the statement also holds for $n + 1$. Hence here: 1) For $n=1: 1+2=3\gt1$ , thus this is true 2) Assume for $n=k: k+2\gt k$. Then for $n=k+1:(k+1)+2=k+3\gt k+1$, thus if we deduct one from both sides we get the inductive hypothesis which we know is true, thus this statement is true as well. Thus we proved what we wanted to.