Subjects/Calculus II/Power series and Taylor series/Term-by-term differentiation and integrationSection 15.2Term-by-term differentiation and integrationWithin ∣x−a∣<R:Copy LaTeXdxdn=0∑∞cn(x−a)n=n=1∑∞ncn(x−a)n−1View detail →FormulaCopy LaTeX∫n=0∑∞cn(x−a)ndx=C+n=0∑∞n+1cn(x−a)n+1.View detail →The radius of convergence is preserved, although the endpoints may change.