One question with Manipulate function

Questions
1

Can anyone tell me how to define a function to produce a sum of n terms with a slider of each term
ex. for 3 terms only
Manipulate[Evaluate[Sum[Subscript[a, i], {i, 1, 3}]], {Subscript[a, 1], 0, 1}, {Subscript[a, 2], 0, 1}, {Subscript[a, 3], 0, 1}]
This previous example is a model of the required function.
I need to define a function of n terms
This is my try
f[n_] := Manipulate[Evaluate[Sum[Subscript[a, i], {i, 1, n}]], Table[{Subscript[a, i], 0, 1}, {i, 1, n}]]

but the problem in the Table function which will produce (for example n=3) {{Subscript[a, 1], 0, 1}, {Subscript[a, 2], 0, 1}, {Subscript[a, 3], 0, 1}}
here the exact problem that the two successive brackets “{{” and, “}}” which should be only one bracket “{” and, “}”
as shown in the attached notebook.
So, please, anyone know how to overcome this problem inform me
Thanks a lot

2

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 ]
3

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]
4

The problem is how to write a correct code for the second argument in Manipulate function as follows
f[n_] := Manipulate[Evaluate[Sum[Subscript[a, i], {i, 1, n}]], …]
i.e. what to be written in the space shown in the above function definition.
in other words it is needed to define a function can generate the following set {Subscript[a, 1], 0, 1}, {Subscript[a, 2], 0, 1}, {Subscript[a, 3], 0, 1}…{Subscript[a, 3], 0, 1} to be written in the Manipulate command