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Explore the controversial mathematical claim that 1+2+3+...=-1/12 in this comprehensive 42-minute video lecture. Delve into non-standard summation methods for divergent series, the eta function, and the concept of analytic continuation. Examine the infamous Numberphile video calculation, identify its flaws, and learn how to correct and connect it to legitimate mathematics. Investigate the Riemann zeta function and its relationship to the series sum. Discover Ramanujan's contributions and calculations related to this topic. Gain insights into advanced mathematical concepts while unraveling the truth behind this puzzling equation. Follow along with detailed explanations, visual aids, and historical context to deepen your understanding of infinite series and their surprising properties.