# How to make a serie ?

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A Achbak on 16 Dec 2020
Edited: A Achbak on 18 Dec 2020
Hi, i need to write a sum of serie :
with b_k= (k+1)^2-(k)^2 and u^(m-k) is the numerical solution approximation u(x,t_m-k) for k=1,...m-1 and m=1,....,20
for m=1:20
syms k u
b(k)=(k+1)^2-k^2;
F=symsum((b(k)-b(k+1))*u(:,m-k),k,1,m-1)
end
F
but i get error
Necessary I need u(:,m-k)

Walter Roberson on 16 Dec 2020
It is never possible to use a symbolic variable as an index in MATLAB.
You need to create a definite list of values and sum() the list. Or loop adding on to a total.
Note by the way that and so b(k) - b(k+1) = (2*k+1) - (2*(k+1)+1) = -2
A Achbak on 17 Dec 2020
You are right !, I'm sorry @Walter Roberson. I just asked my first question in a simple formule of b but your answer is not i want. In fact, it's the same problem with different formule, it's all about calculate the sum of series matrix.
I have a matrix U(:,k). My final question : What is the best way to write the code to calculate sum of series matrix :?
This what i did before
alpha=0.2;b(0)=1.0;c(0)=2.^(1-alpha)-1;
S=U(:,1); %initialize of S
for m=2:20
for k=1:m
b(k)=(k+1).^(1-alpha)-k.^(1-alpha); c(k)=(k+2).^(1-alpha)-(k+1).^(1-alpha);
S=(b(k)-c(k))*U(:,m-k);
end
end
S
I'm sorry again, but I learned a lot from you.

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