Question

Given an example of a statement $P\left(n\right)$ which is true for all $n\ge 4$ but $P\left(1\right),P\left(2\right)$ and $P\left(3\right)$ are not true. Justify your answer.

Answer 1

Consider the statement $P\left(n\right):3n<n!$

For $n=1,3\times 1<1!,$ Which is not true

For $n=2,3\times 2<2!,$ Which is not true

For $n=3,3\times 3<3!,$ Which is not true

For $n=4,3\times 4<4!,$ Which is true

For $n=5,3\times 5<5!,$ Which is true