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