Let C(R) be the space of continuous functions of one real variable
and let
A:C(R)→C(R)
be the operator which maps the function f into the function A(f) defined by
the formula(Af)(x)=1+∫₀^{x}f(t)dt
. Find the limit of the sequence of
functions f,A(f),A²(f),A³(f),... when f (x)=1.for all x∈R