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- Use the equation 1/(1-x) =Σ xn (from n=0 to infinity) for the absolute value of x is less than 1 to expand the function 4/1-x in a power series with the center at c=-2 Then determine the interval of convergenceWhat 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 a power series for the function and the intervals of convergence f(x)=2x/1-x2
- Express the function as the sum of a power series by first using partial fractions. f(x) = x + 4 2x2 − 5x − 3 Find the interval of convergence. (Enter your answer using interval notation.)Now instead integrate the power series for 1/1-x to find a power series representation for ln(1-x0. What is the interval of convergence for this power series? Then use it to determine the exact value of ∞Σ n=0 1/(n+1)2^(n+1).Find the taylor series and interval convergence. 7/3-x ln(1-5x)
- find a power series that represents the function by modifying the base series for 1/1-x Then, find the interval of convergence of the power series:Find a power series for the function, centered at c. f(x)= 2/(5-x). c=-4 determine the interval of convergenceFind the power series and the interval of convergence for f(x)=1/(1-2x)
- Find the power series representation of ln[1 + x] either by differentiation orintegration of the power series or by finding p(x), the Taylor series. Determinethe interval of convergence.Find the first five non-zero terms of power series representation centered at x=0 for the function below. also what is the interval of convergence x2/(1+6x)find1) the power series using transformations of the types A-G of theknown power series of the corresponding elementary function,2) the radius of convergence,3) the interval of convergence,4) the 7-th derivative of f(x) at x = 0.