Working with binomial series Use properties of power series, substitution and factoring to find the first four nonzero terms of the Taylorseries centered at 0 for the following functions. Give the interval of convergence for the new series. Use the Taylor series

Solution 40EStep 1:In this problem we need to find the first four nonzero terms of the taylor series centered at ‘0’ for the function by using the taylor series : = 1+- +-............., for -1 < x , and interval of convergence of the new series.Consider , = = 2 ) , since = 2By , using for -1 < x we get = 2 ) = 2( ) , for -1< ( ) = 2( ) , for -1< ( ) ,since ) if n is odd. = 2( ),for -1< ( ) = 2( 1-,for -1< ( ) = 2-,for -1< ( ) Therefore...