proof explanation - Value of the Riemann Zeta Function for

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

The Secrets Of The Universe - #Equations#40 The 40th Equation of the series is on the famous Riemann Zeta Function. This function first appeared in the first half of the 18th century

The Riemann Zeta Function

The Riemann Zeta Function and Probability Distributions – Almost Sure

the Riemann Hypothesis - Clay Mathematics Institute

Why do all of the non-trivial zeroes of the Riemann zeta function have real part of [math]1/2[/math]? - Quora

PPT - Riemann Zeta Function and Prime Number Theorem PowerPoint Presentation - ID:2712330

PDF) Will a physicist prove the Riemann Hypothesis?

number theory - Some confusion about the complex logarithm and the Riemann zeta function - Mathematics Stack Exchange

Derivation of the reflection integral equation of the zeta function by the complex analysis

The Extended Riemann Hypothesis and Ramanujan's Sum

Solved The Riemann zeta function is defined via the series

Solved 10. Prove that Riemann zeta function ζ(x)=∑n=1+∞nx1