After reading more carefully about the subscripted terms, something like the following?
(* Mathematica 7 *) f[n_] := Sum[ Subscript[a, j], {j, 0, n}](*Define the function*) Manipulate[ f[n], {n, 0, 4, 1}, ControlType -> RadioButton]
Something like this?
(* Mathematica 7 *) f[x_] := 1 + 2 x + 3 x^2 + 4 x^4 (*Define the function*) Manipulate[ Take[f[x], n](*Take n terms*)/. x -> m (*replacing x with some value m*), {n, 1, 4, 1}, {m, 1, 3, 1}, SaveDefinitions -> True, ControlType -> RadioButton ]
