How do you find the maximum error in series?

clear all, close all

%Case 1: Find FN for N (being a value based on a user's input)
FN = 0; x=.75;
 prompt = 'What is the value of N? ';
 N = input(prompt);
      for n = 1:N
        FN = FN + (((-1)^(n+1))*(x^n))/(n);
      end
      fprintf(' Case 1: Value of FN for N = %4i is %6i \n\n',N,FN)

%   Case 2:  Find maximum value of N such that FN <= ln(1.75)
      LN = log(1+x);  FN = 0;   n = 2;
      while FN > LN
        n = n+1;
        FN = FN + (((-1)^(n+1))*(x^n))/(n);
      end
      N = n;
      fprintf(' Case 2: Value of FN = %6i for N = %4i  \n\n',FN,N)
%
%   end of program

THE FIRST CASE OF THE PROGRAM WORKS HOWEVER I CANNOT FIGURE OUT HOW TO FIND THE MAXIMUM VALUES THAT "N" CAN BE.