{"id":"series-and-convergence","domain":"analysis","type":"Concept","title":"Series & Convergence","slug":"series-and-convergence","url":"/mathematics/analysis/series-and-convergence/","summary":"Infinite sums that may converge to a finite value or diverge. Resolves Zeno's Paradoxes; basis of Taylor series and the Basel Problem.","added_to_codex":"2026-05-27","last_verified":"2026-05-27","sources":[{"tier":1,"citation":"Rudin, W. (1976). Principles of Mathematical Analysis. 3rd ed."},{"tier":1,"citation":"Knopp, K. (1990 reprint). Theory and Application of Infinite Series. Dover."},{"tier":2,"citation":"Hardy, G.H. (1949/1991). Divergent Series. Oxford/Dover."},{"tier":3,"citation":"Dunham, W. (1999). Euler: The Master of Us All. MAA."}],"relationships":[{"type":"built_from","target":"limit","label":"Limit"},{"type":"related_to","target":"derivative","label":"Derivative — Taylor series"},{"type":"generalised_by","target":"riemann-hypothesis","label":"Riemann Hypothesis — zeta function"},{"type":"resolves","target":"zenos-paradoxes","label":"Zeno's Paradoxes"},{"type":"used_by","target":"madhava","label":"Mādhava"}],"entry_status":"live","reading_levels_available":["curious","exploring","deep_dive"],"completeness":1.0,"codex_version":"1.8"}