f( x ) = ( 2 + x )/( 1 - x ) = 2/( 1 - x ) + x/( 1 - x ) =

= 2*sigma( x^n ) + x*sigma( x^n ) // n goes from 0 to infinity

= 2*( 1 + x + x^2 + ... ) + x*( 1 + x + x^2 + ... ) =

= 2 + 2*( x + x^2 + x^3 + ...) + ( x + x^2 + x^3 + ... ) =

= 2 + ( 2 + 1 )*( x + x^2+ x^3 + ... ) =

= 2 + 3*sigma( x^n ) // n goes from 1 to infinity