proof explanation - Value of the Riemann Zeta Function for negative integers - Mathematics Stack Exchange

I am reading the book "Riemann's Zeta Function" by H. M. Edwards. I had a confusion in Section 1.5, Page 12 at the derivation of the formula of Riemann Zeta Function at negative integers

PDF) Proof of Riemann hypothesis

PDF) Values of the Riemann zeta function at integers

number theory - Some confusion about the complex logarithm and the

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How is the Riemann zeta function zero for negative even integers

real analysis - Riemann zeta function - Mathematics Stack Exchange

complex analysis - About the video The Riemann Hypothesis

On Cryptography and the Zeta Function, by Bob McElrath

On Cryptography and the Zeta Function, by Bob McElrath

Particular values of the Riemann zeta function - Wikipedia

Riemann zeta function - Wikipedia

Negative values of Riemann zeta function on the critical line

PDF) Proof of the Riemann Hypothesis

Riemann Zeta Function -- from Wolfram MathWorld