Subjects/Calculus II/Fundamental Maclaurin series/Formula15.5. Fundamental Maclaurin seriesFormulaIn 15.5. Fundamental Maclaurin seriesFormulaCopy LaTeXarctanx=n=0∑∞(−1)n2n+1x2n+1,∣x∣≤1VariablesxVariable independiente (variable de integración)nExponente o índice enteroConditions∣x∣≤1Related formulasRelatedFormulaln(1+x)=n=1∑∞(−1)n−1nxn,−1<x≤1Open formulaOpen in sectionRelatedFormula1−x1=n=0∑∞xn,∣x∣<1Open formulaOpen in sectionRelatedFormulacosx=n=0∑∞(−1)n(2n)!x2n=1−2!x2+4!x4−⋯Open formulaOpen in sectionRelatedFormulasinx=n=0∑∞(−1)n(2n+1)!x2n+1=x−3!x3+5!x5−⋯Open formulaOpen in sectionRelatedFormulaex=n=0∑∞n!xn=1+x+2!x2+3!x3+⋯Open formulaOpen in section