central limit theorem

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

Var(x₁+x₂+...+x_n} --> ? as n--> infinite.

please give the answer.

in my book, Var(x₁+x₂+...+x_n} --> infinite as n--> infinite, but i think Var(x₁+x₂+...+x_n} --> 0 as n--> infinite. thanks.