MATLAB: Hello i have an iteration table for a maclaurin series, can anyone tell me what’s the coding to make a table like this

maclaurin

Best Answer

There are several ways to calculate a series in MATLAB. From your question, you appear to be a beginner, so I will show an intuitive way using for-loop.
term_n = @(x,n) x^n./factorial(n); % formula for n-th term of series
N = 10; % total number of terms we are going to calculate
result = zeros(1,N+1); % initializng a array to save the partial sums
eplison_t = zeros(1,N+1);
eplison_a = zeros(1,N+1);
x = 1/2; % value of x to use in this calculation
result(1) = term_n(x,0); % calculate first term of the series at n=0
eplison_t(1) = (exp(x) - result(1))/exp(x);
for n=1:N % terms n=1,2,...,N
    result(n+1) = result(n) + term_n(x,n); % current partial sum is the addition of last partial sum and the value of n-th term
    eplison_t(n+1) = (exp(x) - result(n+1))/exp(x);
    eplison_a(n+1) = (result(n+1)-result(n))/result(n+1);
end
eplison_t = 100*eplison_t;
eplison_a = 100*eplison_a;
t = table(result', eplison_t', eplison_a');
disp(t)
Result
>> test_fun
     Var1        Var2          Var3   
    ______    __________    __________
         1        39.347             0
       1.5        9.0204        33.333
     1.625        1.4388        7.6923
    1.6458       0.17516        1.2658
    1.6484      0.017212       0.15798
    1.6487     0.0014165      0.015795
    1.6487    0.00010024     0.0013163
    1.6487    6.2197e-06    9.4018e-05
    1.6487    3.4355e-07    5.8761e-06
    1.6487    1.7097e-08    3.2645e-07
    1.6487     7.741e-10    1.6323e-08
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