= 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.)

Expand the function in a power series anx" with center c = 0. Find anx". 8+7x n=0 (Express numbers in exact form. Use symbolic notation and fractions where needed. For alternating series, include a factor of the form (-1)" in your answer.) anx" %3D 8 Incorrect

use Series to evaluate メ (1- 2x)²

Write the given function as a power series and give the interval of convergence. b.) f(x) == 5-x

For each series, determine whether it converges absolutely. converges conditionally, or diverges. (a) (-1)" sin(n) n3" (-2)"-3" (b) iMiM

how would i write this as a power series??

Find the series' interval of convergence and, within its interval, the sum of the series as a function of ?x.

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.

Evaluate by series approximation

+(-1)". (X-2)h 2 h+1 Fex) =Ź (x-2) _(x-2) --a. 4 Findea a.values of (x) that make series converged. la. The of series. Note with an explanation of the StePs