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Calculate the sum of a series

User: "Dung the most handsome man"
Altair Community Member
Updated by Dung the most handsome man

Hi everyone,


the picture below is the sum of a series that have infinity limit, and i don't know the suitable function to deal with the problem.
image.png.640551bd8b4f85f175147f07cb199eb8.png

Thanks for your help.

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    User: "L Moretti"
    New Altair Community Member
    Updated by L Moretti

    Hi Dung,

     

    you can try this:

     

    clc, clear
    Sum = 0;
    for k=1:100000
        Sum = 1/k^2 + Sum;
    end

    User: "Dung the most handsome man"
    Altair Community Member
    OP
    Updated by Dung the most handsome man

    Thank you, but i need the more accuracy result, cause exactly, the result is pi^2/6. I tried your solution before, the result is an irrational number.
    Anyway, thanks for your suggest.

    User: "manoj kandukuri"
    Altair Employee
    Updated by manoj kandukuri

    Hi Dung,

    you can get more accurate result by having a tolerance condition inside a while loop. something like below:

     

    %%

    clc, clear
    sum = 0;
    sum_before = realmax;
    tol = 1e-12;  % tolerance value
    i = 0;

    while (abs(sum_before - sum) >= tol) 
        i= i+ 1;
        sum_before = sum;
        sum = sum + 1/(i^2);        
    end 

    %%

    Hope this helps

     

    Thanks,

    Manoj kandukuri