If 1>r>0 then the sequence r^(1/n) converges to 1.
So if glb(x_n)>0 that would contradict the given that a<1.
Now use the fact the glb(x_n)=0 to prove the statement.
I am having trouble proving this problem.
Let (xn) be a sequence of positive numbers such that lim [(xn)^(1/n)] exists and equals a. a is greater than 0, but less than 1. Prove that lim (xn) = 0.
The limits are to inf.