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