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

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

please give the answer.

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