Answer
See below.
Work Step by Step
Proofs using mathematical induction consist 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 we have:
1) For $n=100: 100(100)=10000\leq100^2=10000$
2) Assume for $n=k: 100k\leq k^2$. Then for $n=k+1\geq101$:
$100(k+1)=100k+100\leq k^2+100\leq k^2+2k+1=(k+1)^2$
Thus we proved what we wanted to.