Find the Taylor series for f centered at 7 if (-1)^n! 3n (n + 1) f(n) (7) = n = 0 What is the radius of convergence R of the Taylor series? R =
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- Find the Taylor series for f centered at 4 if f^(n)(4) = (-1^n)n!/3^n(n+2) What is the radius of convergence R of the Taylor series?What are the first non-zero terms of the Taylor series, the power series written in sigma notation, and the interval of convergence for the function f(x)=ln(1+4x) with a=0?Find the Taylor series of the functionf(x) = ln(1 + 2x)−ln(1−2x) at x= 0. Find the interval of convergence for the Taylor series.
- What is the radius of convergence of the Taylor series for (x2 − 2x + 2) − 1 about x = 0? about x = 1?Find the nth Partial Sum Sn of the series and also discuss convergence/divergence of the seriesGive the Taylor series expansion of f(x) = ln(4-x) at the center a=3. Determine its interval of convergence. Approximate ln(3) using the first 7 terms of the expansion.