Summation with For LOOP (iterations)

so this is the summation I am working with. I have four constants of ki and zi. I am looking for (V/F). I think I am suppose to use iterations to find the answer? I don't really know. Any advice to get stated will really help.

ki=[56, 0.65, 0.175, 0.055];

zi=[0.5, 0.1, 0.15, 0.25];

xl=0;

for i=0.1:length(1)

xl=xl+(zi(ki-1))/(1+i(ki-1));

end

What I did so far.... (replaced V/F with i)

[madhan ravi]

Aren't V and F supposed to be scalars?

[Rebecca Reyes]

I really dont know. The answer for V/F=.59 if done correctly.

Answer 1

[Jan]

K = [56, 0.65, 0.175, 0.055];
Z = [0.5, 0.1, 0.15, 0.25];
fcn = @(x) sum(Z .* (K - 1) ./ (1 + x * (K - 1)))
fzero(fcn, 0.5)
% 0.591015474362563

There are some more zeros: at 1.15928465237477 and 2.63599135955416. See:

fplot(fcn)

[Rebecca Reyes]

Hi! thank you for answering! but is there any way I can solve for the equation using a for or while loop? initial guess for V/F is 0.1

[Rebecca Reyes]

sorry i didnt ask clearly before

[Jan]

@Rebecca Reyes: Your questions about Matlab are welcome. If all details are clear already, it would not be a problem anymore.

Of course you can find the solution by your own with a loop also. Implement a Newton-Raphson-method. You can get the differentiation of the function numericalls. A colleague of mine has implemented this for large systems and published the code as his PhD. Of course an iterative solver for small problem can be written with less than 100 lines of code also, but it is not as trivial as "using a FOR oder WHILE loop".