用Octave求泰勒展开（5）
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常见麦克劳林展开式（5）
\(\frac{1}{1+x}=1-x+x^{2}-\cdots+-1^{n}x^{n}+o(x^{n})\)
求\(\frac{1}{1+x}\)的泰勒展开.
程序代码如下
function [text_result, numeric_result] = func43(order)
    pkg load symbolic;
    x = sym('x');
    question = 1 / (1 + x);
    d = taylor(question, 'order', order + 1);
    text_result = ["\n", disp(d)];
    numeric_result = eval(d);
endfunction
计算5阶泰勒展开，结果如下
>> [text_result, numeric_result] = func43(5)
text_result =
       5    4    3    2
    - x  + x  - x  + x  - x + 1

numeric_result = (sym)

       5    4    3    2
    - x  + x  - x  + x  - x + 1
计算10阶泰勒展开，结果如下
>> [text_result, numeric_result] = func43(10)
text_result =
     10    9    8    7    6    5    4    3    2
    x   - x  + x  - x  + x  - x  + x  - x  + x  - x + 1

numeric_result = (sym)

     10    9    8    7    6    5    4    3    2
    x   - x  + x  - x  + x  - x  + x  - x  + x  - x + 1
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