Riemann Hypothesis Using Simple Inequality

The Riemann Zeta function is defined as \\ \large \zeta(s)= $$\sum_{n=1}^{\infty} 1/n^{s}$$ , Re(s)$$>$$1 \\ The Zeta function is holomorphic in the complex plane except for a pole at \\ s=1. The trivial zeros of \zeta(s) are -2,-4,-6,... . Its non trivial zeros lie in \\ the critical strip 0< Re(s)< 1 .\\ The Riemann Hypothesis states that all the non trivial zeros lie on the critical line \\ Re(s)=1/2.\\