Sum of series with a variable

I have the function , where are i-th components of given vectors respectively. I need to implement it Matlab and find the roots. I tried to use sum in a for loop and then fzero:

alpha = 0.5;
sum = 0;
for i = 1:n
    sum = @(x) sum + y(i)^2/(z(i) - x)
end
fun = @(x) 1+alpha*sum
lambda = fzero(fun,0)

but it's not working. Any ideas how to fix this?

Answer 1

[David Hill]

I always like to look at what I am doing before solving. Numerially, it should be relatively easy to find the root.

alpha = 0.5;
f=@(x)1+alpha*arrayfun(@(a)sum(y./(z-a)),x);
x=-100:100;
plot(x,f(x));