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- Find the radius of convergence and interval of convergence of the series X∞ n=1 xn 3n n6What is the radius of convergence of the Taylor series for (x2 − 2x + 2) − 1 about x = 0? about x = 1?compare the series (1+x)-3=1-3x+6x2-10x3........ with ex= 1+x +x2/2 +x3/6............ Are they both convergent? How can you prove this?
- Find the radius of convergence and interval of convergence of the power series ∞∑n=0(x+3)nn!.Find a power series for the function, centered at C and determine the interval of convergence (function is h(x) and C = 0).h(x)=1/(1-5x) Also see the attached picture of the problem.find a minimum value for the radius of convergence of a power series solution about x0
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