Zeros and the pole of the Riemann zeta function ζ(s) correspond to simple poles of the logarithmic derivative f(s) = d/ds ln ζ(s). In Re{s} > 1 the function f (s) has an absolutely convergent sum expression and an analytic continuation to the complex plane except for a discrete set of simple poles in the area Re{s} ≤ 1. Close to a pole sk the function f (s) is rk /(s−sk)+finite terms. Omitting the finite terms, we can evaluate this function into a Taylor series at the x-axis point x > 1. The absolute values of the coefficients of the Taylor series of each pole decrease as x−i for some i > 0 as a function of x. The absolute values of the coefficients of the Taylor series of f (s) decrease as a negative exponent of x when x grows. That means that all terms aix−i, ai ∈ IR, are cancelled by other terms in f (s) when x → ∞. These other terms must contain terms −aix−i. Such terms arise only from poles. It follows that in the sum of all poles of f (s), at the point x, poles must cancel other poles when x → ∞. The poles of f (s) in Re{s} ≥ 1 and Re{s} ≤ 0 are known. They are the only poles that give a negative coefficients of x−j , j > 0, while the remaining poles, the non-trivial zeros of ζ(s), give positive coefficients. It is shown that the poles of f (s) cancel when x → ∞ if and only if every pole sk at 0 < Re{sk } < 1 satisfies Re{s} = 1 2 , i.e., the Riemann Hypothesis is true.