Representing functions by power series Identify the functions represented by the following power series.

Solution 54EStep 1:In this problem we need to identify the function represented by the power series Consider , = ++++........... = -+-+........... Is an infinite geometric series , here “ the first term (a) = x , and the common ratio (r)= = We know that a+ar+ Then () = , if |r|< 1 , , if |r| > 1 Therefore , -+-+........... . is an infinite geometric series, then = = = = f(x) . Therefore , the function f(x) = represented by the power series