I have positive random variables X1, X2, X3, ..., Xn such that their sum=1 (so they are random, subject to constraints that each Xi is positive their sum has to be 1.. so all are fractions).

Now, I have a function f=C1.X1+C2.X2+C3.X3.....+Cn.Xn

where C1, C2, ....Cn are known coefficients (real numbers).

My question is: if n tends to infinity, will f converge to some number? Is there any law in statistics which talks about such a scenario?

Thanks.