=(- 1)^(n- 1)*4n/(2n- 1)*(2n+ 1)

=(- 1)^(n- 1)*[((2n+ 1)+(2n- 1))/(2n- 1)*(2n+ 1)]

=(- 1)^(n- 1)*[(2n+ 1)/(2n- 1)*(2n+ 1)+(2n- 1)/(2n- 1)*(2n+ 1)]

=(- 1)^(n- 1)*[ 1/(2n- 1)+ 1/(2n+ 1)]