Calculate and display the value of the function F(x) on the interval [a,b]. How to solve this?

Question

Algorithms

Calculate and display the value of the function F(x) on the segment [a,b] with an accuracy of e.
F(x) = 1 + (x/3) + pow((x/3),2)... [0, 0.9], at step 0.1
I'm not so much interested in the algorithm itself as in understanding what is needed from me here.
How to bring it to a recurrent form? Specifically, I can compose the algorithm itself, you just need to understand at what point you need to exit the loop.
Well, in general, a general understanding of the solution of such problems.

Answer 1

The recurrent form is not required here, the simplest cycle from and to with a given step.