How to change the previous result ?

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Hi, I want to compute the solution : for n=2,... where . With the initial solution .
For example :
if n=2, then
if n=3, , it's possible to rewrite S as : where S is the previous result has stored but have to replace with , then compute
if n=4, , it's mean where S is the previous result has to replace with and with .
and continue .....
Here what i did :
S = 0;
U1 = 5;
k = 0;
for n=2:10
% Compute the sum term
k = k+1;
b = sqrt(n-k+1)-sqrt(n-k);
S = S+b*U1;
% Compute the new solution
U = S+10;
% Overwrite the solution to change the result of the sum S : S = b*U;
% without use the index U(i)
U1 = U;
% but it's not correct
end
What I do ?

采纳的回答

Sulaymon Eshkabilov
There was an err inside the loop. Here is the corrected complete and simplified code:
S = 0;
U = 5;
for n=2:10
b = sqrt(n)-sqrt(n-1);
S = S+b*U;
U = S+10;
end
fprintf('Final values: S = %f and U = %f \n', [S, U])

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