Subjects/Calculus II/Power series and Taylor series/Fundamental Maclaurin seriesSection 15.5Fundamental Maclaurin seriesFormulaCopy LaTeXex=n=0∑∞n!xn=1+x+2!x2+3!x3+⋯View detail →FormulaCopy LaTeXsinx=n=0∑∞(−1)n(2n+1)!x2n+1=x−3!x3+5!x5−⋯View detail →FormulaCopy LaTeXcosx=n=0∑∞(−1)n(2n)!x2n=1−2!x2+4!x4−⋯View detail →FormulaCopy LaTeX1−x1=n=0∑∞xn,∣x∣<1∣x∣<1View detail →FormulaCopy LaTeXln(1+x)=n=1∑∞(−1)n−1nxn,−1<x≤1−1<x≤1View detail →FormulaCopy LaTeXarctanx=n=0∑∞(−1)n2n+1x2n+1,∣x∣≤1∣x∣≤1View detail →with conditional convergence at x=±1 depending on the corresponding value.