Let $G$ be a graph of order $n$ with $\kappa (G) \geq 1$. Prove that $n> \kappa(G)[\operatorname{diam}(G)-1]+2$

Question

Let $G$ be a graph of order $n$ with $\kappa (G) \geq 1$. Prove that $n> \kappa(G)[\operatorname{diam}(G)-1]+2$

I know $\kappa(G) \leq n-1$. I do not know if do we have to prove it by induction or there is another way.