Coding taylor approximation of natural log

Question

jLeo 2019-2-11

0
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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/444367-coding-taylor-approximation-of-natural-log

评论： jLeo 2019-2-11

Hi all,

I need to approximate ln(1.9) using a taylor series ln(1-x)=Sum(-(x^k)/k,k,1,inf). I have to code a script to figure out 1) how many terms I need, 2) the value from the series, and 3) the error. Here is what I have so far. I tried to run it, but it seems to be not ending.

x=0.9;
target_equation = log(1-x);
series_sum = 0;
difference = abs(target_equation - series_sum);
threshold = 1*10^-10;
count = 0;
while difference > threshold;
    count=count+1;
    series_sum=series_sum + ((x^count)/count);
    difference = abs(target_equation - series_sum);
end
disp(series_sum);

I'm not sure what is wrong with my code. Any suggestion?

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Answer 1

RAMAKANT SHAKYA 2019-2-11

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https://ww2.mathworks.cn/matlabcentral/answers/444367-coding-taylor-approximation-of-natural-log#answer_360568

在 MATLAB Online 中打开

if you want to calculate log(1.9) and x=0.9 then you have apply taylor series log(1+x) see formula form google and change in to the code is

function series_sum=talor(x)  %give x=0.9 as input
target_equation = log(1+x); % for calculating log(1.9)
series_sum = 0;
difference = abs(target_equation - series_sum);
threshold = 1*10^-10;
count = 0;
while difference > threshold;
    count=count+1;
    series_sum=series_sum + ((-1)^(count+1)*(x^count)/count); %as per formula of taylor series the even term cofficients are negative
    difference = abs(target_equation - series_sum);
end
disp(series_sum);