The question uses the phrase "recurrence relation" only twice, and the second occurrence refers to the first one. To derive this recurrence relation, you need to know what f is. I think you need to apply Newton's method to this f.
I'm sorry but the question is in the attachment because I seem to have a problem uploading equations in fractions. If you refer to the question, I'm not sure whether the 'above recurrence relation' refers to the one in V_{n} or f(V_{n}), but assuming it's the one in f(V_{n}), I tried comparing the gradients of the tangent [f'(V_{n}) = f(V_{n})/ (V_{n} - V_{n+1})] but I don't know how to proceed from there.
Please help me and sorry for the inconvenience caused!
The question uses the phrase "recurrence relation" only twice, and the second occurrence refers to the first one. To derive this recurrence relation, you need to know what f is. I think you need to apply Newton's method to this f.