Proving ζ(-1)=-1/12 for Mathematicians

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Proving ζ(-1) = -1/12 involves defining the zeta function for negative integers, which is the challenging aspect of the proof. Once the zeta function is appropriately defined, the equation can be derived relatively easily. A recommended resource for a solid proof is found in Godement's book, specifically in Chapter VI.2.19. The discussion highlights the importance of understanding the zeta function's extension to negative values. This foundational knowledge is crucial for mathematicians exploring this equation.
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How can one prove the above equation?
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