$(20$ points$)$ Consider a market with n risky assets S$1,$ S$2,...,$ Sn and a bond B$.$ Investments are made at time $0$ and returns are collected after T years. Let $1,...,$ n be the beta factors of the assets in the CAPM Theorem $($i$.$e$.$ i is the beta factor of a portfolio consisting only of Si$),$ and V be the beta factor of an arbitrary portfolio V with weight wi on the risky asset Si for every i$.$ Prove that:

V $=$ w$1$$1+$ w$2$$2+...+$ wnn