How to change the previous result ?

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 ?

Answer 1

[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])