for the sequence {x_{n}} of independent and uniformly bounded r.v's, both WLLN and CLT holds provided

Var(x_{1}+x_{2}+...+x_{n}} -->?as n--> infinite.

please give the answer.

in my book, Var(x_{1}+x_{2}+...+x_{n}} -->infiniteas n--> infinite, but i think Var(x_{1}+x_{2}+...+x_{n}} -->0as n--> infinite. thanks.