Manipulate[Plot[{(1/(1-x)),(∑_(i=0)^n)x^i}, {x, -1.1,1}, PlotStyle -> Thickness[.005],PlotRange ->{-1, 5.02}, AxesLabel ->{x,y}, PlotLabel-> "y = (1/(1 - x)) and the Taylor Polynomial y = (Subscript[P, n])(x)", Epilog -> {Point[{-1,1}], Point[{-1,0}], Point[{1,1}], Point[{1,2}], Point[{1,3}], Point[{1,4}], Point[{1,5}]}], {{n,1}, Range[0,10,1]}, ControlType -> Setter]

Manipulate[Plot[ (1/(1-x)) - (∑_(i=0)^n)x^i, {x, -1.1,1},PlotStyle -> Thickness[.005], PlotRange ->{-1, 1}, AxesLabel ->{x,y}, PlotLabel -> "Error of Taylor Polynomial: y = (1/(1 - x)) - (Subscript[P, n])(x)", Epilog -> {Point[{-1,.5}], Point[{-1,-.5}]}], {n, Range[0,10,1]}, ControlType -> Setter]