Find recurrence relation please help!

[louisatanhuiying]

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!

 

[Deleted member 4993]

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!

This follows the Newton-Raphson algorithm for finding roots of polynomials.

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