How to calculate this Sum :

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HAli 2018-1-26

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https://ww2.mathworks.cn/matlabcentral/answers/379148-how-to-calculate-this-sum

评论： HAli 2018-1-30

sum.png

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Jan 2018-1-27

This is not "one" sum, but n different sums according to the index i. Do you want a numerical or symbolical summation? Please explain,what the inputs are, what you want as output and post the code you have tried so far.

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Torsten 2018-1-26

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https://ww2.mathworks.cn/matlabcentral/answers/379148-how-to-calculate-this-sum#answer_301914

Google "telescoping sum".

Best wishes

Torsten.

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HAli 2018-1-26

Hi thanks for your answer,but "telescoping sum"explain just a sum ,my problem is to solve a sum+another term!

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Torsten 2018-1-26

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https://ww2.mathworks.cn/matlabcentral/answers/379148-how-to-calculate-this-sum#answer_301919

在 MATLAB Online 中打开

yes, add the other term to the value of the telescoping sum. What's the problem ?

In your case, your complete expression from above equals

l_(i)*(r_(i)+2*r_(i+1)) + r_(i)^2 - r_(n)^2

Best wishes

Torsten.

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HAli 2018-1-28

在 MATLAB Online 中打开

I'm sorry Jan, but I try my best !!

you told me where the term came from: B0(i,j)=f_n+(1/3)*l_(i)(r_(i)+2*r_(i+1));*

Because these are the terms of my Matrix that I named B0 : its not just a sum,but a sum (from i to n-1) + another terme just depends on i

So,for the first term of the matrix B0, I have these terms analytically:

So,I changed the code another time, using your proposal:

 B0=zeros(n,n);
for i=1:n
            l(i)=0.042;
            r(i+1)=r(i)+delta;
end
 S=0;
for i=1:n
for j=i:i
    for k=i:n-1
        S = S+r(k)^2-r(k+1)^2;
        B0(i,j)=S+(1/3)*l(i)*(r(i)+2*r(i+1));  
        B0(i+1,j)=-(S+(1/3)*l(i)*(r(i)+2*r(i+1)));        
    end
       end
end

but this program is not correct because it doesn't sum up in a correct way,he had to make the sum of r(k)^2 -r(k+1)^2 from i (the value of i depends on the line i of the matrix) to n-1 (+) the second term which (1/3)*l(i)*(r(i)+2*r(i+1) depends just on the line i of the matrix.

For example,for line i =3 of the matrix B0:

it has to sum the r(k)^2 -r(k+1)^2 of i = 3 to n-1 and add the second term (1/3)*l(i)*(r(i)+2*r(i+1) just for i = 3

N.B:I changed the variable of the sum j by k because the matrix is always defined by i (the rows) and j (columns),

HAli 2018-1-30