Q.Prove that $2^n > n$ for all positive integer.

Some statements proved by induction are inequalities rather than equalities — for instance $2^n > n$ for all positive integers $n$, or Bernoulli's inequality $(1+x)^n \ge 1 + nx$ for $x > -1$. The base case checks the inequality directly for the smallest $n$, and the inductive step assumes the inequality holds for $n = k$ and must show it holds for $n = k+1$. Because inequalities are not preserved simply by "adding the same thing to both sides" the way equalities are, the inductive step for an inequality typically multiplies or bounds …