= 0.) Express the function as the sum of a power series by first using partial fractions. (Give your power series representation centered at x = f(x) = n = 0 2x8 f(x) = 2 x² + 8x + 7 Find the interval of convergence. (Enter your answer using interval notation.)

Let f(x) = 1 + x 1 X Find the power series representation for the function f(x) by completing the following steps: a. First, express the fraction 1¹ as a power series. = X b. Now, express the fraction as a power series. 1-x 1+x x c. The function f(x) 1-x 1-x + 1 is the sum of the two series from parts (a) and (b). Express the function f(x) as a power series. d. What is the interval of convergence and the radius of convergence for this power series?

how would i write this as a power series??

From the following statements, choose the one(s) that are true. OA. The function f(x) = can be represented by the power series (- 1)"2"x2. 1+2x O B. The function f(x) = 1 can be represented by the power series 1 2+2x 2 OC. x"+1 00 The function f(x) = In(1+ x) can be represented by the power series O D. The power series Ln = 0 n! converges only when X=0 and has a radius of convergence of R=0. OE. The function f(x) = In(1- x) can be represented by the power series * n+1 OF. The power series *n! xn converges only when x=0 and has a radius of convergence of R=0.

For the function ln(5x+11), (a) write a power series representation of the function, (b) find the center and radius of convergence of the power series from (a), and (c) find the interval of convergence of the same power series.

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Find the radius of convergence, R, of the series. R = 8 I = n = 1 n²x^ 3 6 9 (3n) Find the interval, I, of convergence of the series. (Enter your answer using interval notation.