Prove by mathematical induction that $n^2 > n$ for all $n \geq 2$.
My attempt:
When $n=2$
LHS , $2^2 =4$
RHS , $2$ When $n=2$, LHS $>$ RHS
Assume true for $n=k$
$k^2>k$
RTP true for $n=k+1$
$(k+1)^2 > k + 1$
Proof
By assumption
$k^2>k$
Thus, $k^2 +2k +1 > k + 2k +1 $
$(k+1)^2 > (k+1) + 2k $
Since $k > 1$
$2k>2 $
Hence $(k+1) + 2k > k+1 $
Therefore $(k+1)^2 > k+1$
Hence by induction the statement is true