# Linear combination: Trying to calculate a weighted outcome

I have a basic question: if you have a linear combination of two vectors u, v where u = $\begin{bmatrix} a_1 \\ \vdots \\ a_n \ \end{bmatrix}$ and v = $\begin{bmatrix} w_1 \\ \vdots \\ w_n \ \end{bmatrix}$ and where $\ w_1+w_2+\cdots+w_n = 1$ and $\ w_1, w_2, \ldots ,w_n$ are all positive real numbers and $\ a_1, a_2, \ldots ,a_n$ are all positive integers.

My question: Does $u \cdot v$ converge to say a real number A no matter the size of $n$?

• If the vector space has finite dimension, any product $u\cdot v$ will converge. – jobe Apr 5 '18 at 14:27
• What do you mean by "converge" here? What is the sequence? $u\cdot v$ is just a real number by definition. – wgrenard Apr 5 '18 at 15:08
• So really does there exist a limit A for u⋅v as n goes to infinity? – Se7venn Apr 5 '18 at 20:57