Given that x 1-7 1-7x5° ∞ n=0 1 1 x n=0 x with convergence in (-1, 1), find the power series for The radius of convergence is

Consider the series (-1)-¹(x+1)" where b is a given non-zero constant. Find the nb2n J=0 interval of convergence for the series. Express your answer in terms of the constant b. Make sure you show the steps for obtaining your answer. Don't forget to check the end points of the interval.

Represent the function (10)/(1-2x)^2 as a power series. Find: c0, c1, c2, c3, c4, and the radius of convergence R.

Express the function as the sum of a power series and find the radius of 1- 3 convergence and interval of convergence.