Number of terms needed for Maclaurin series expansion (while loops)

Given the above problem, I've attempted to code this different ways based on what I knew and from the methods I found on the Internet.

    function [ numOfTerms ] = lnOfOnePlusX( x )

    actual=log(1+x);
    n=1;
    index=1;
    summation=0;
    difference=0;
    % Calculating first term
    approx(index)=(((-1)^(n+1))/n)*(x^n);

    % Calculating the subsequent terms
    n=n+1;
    index=index+1;
        while difference>=0.001
            approx(index)=(((-1)^(n+1))/n)*(x^n);
            summation=summation+approx(index);
            difference=abs((approx(index)-approx(index-1))/approx(index));
            n=n+1;
            index=index+1;
        end

    end

We've not discussed the use of index before in class but it was on another MATLAB Answers page that was trying to implement Taylor series for something else.

Here's another set of code that I tried and it still didn't work. This one gives me an infinite loop because the while condition is always met, it seems like. I just don't have the function part because it was easier to work with.

    clear, clc
    x=0.1;

    actual=log(1+x);
    approx=x;
    n=1;

    difference=abs((actual-approx)/actual);
    threshold=1E-3;

        while difference>=threshold
            n=n+1;
            approx=approx+(((-1)^(n+1))/n)*(x^n);
            difference=abs((actual-approx)/actual);

        end

With x=0.1, we are there's supposed to be 3 terms. x=0.2: 4 terms. x=0.5: 7 terms. x=0.9: 31 terms.

[Walter Roberson]

+1 for taking the time to give your trial code and describing the difficulty you are observing.