Calculate taylor series using while loop

Question

Fabian Schön 2021-11-23

1
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https://ww2.mathworks.cn/matlabcentral/answers/1593889-calculate-taylor-series-using-while-loop

评论： Fabian Schön 2021-11-25

I want to calculate the taylor series of ln(5) using a while loop.

x = 1/5;
tol = 1e^-9;
s = 0;
i = 0;
term = (x-1)
while abs(term) > tol
    s = s+term;
    i = i+1;
    term = (-1.^i)*(((x-1).^i)./1);
end
disp(s)

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Dyuman Joshi 2021-11-24

编辑：Dyuman Joshi 2021-11-25

Why are you defining x = 1/5 when you are calculating expansion for the value 5?

Also, the formula for term in the loop is incorrect.

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Answer 1

James Tursa 2021-11-25

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https://ww2.mathworks.cn/matlabcentral/answers/1593889-calculate-taylor-series-using-while-loop#answer_840054

编辑：James Tursa 2021-11-25

Looks like you are planning to use the identity ln(5) = ln((1/5)^-1) = -ln(1/5) and then use 1/5 as the x in the Taylor Series expansion that is good for 0 < x <= 2. However, the problems are:

The divisor in your term needs to be i, not 1
The initial value of i should be 1, not 0
The -1 factor needs to be wrapped in parentheses and have a different exponent, i.e. (-1)^(i-1)
Per above, you need to display -s, not s