Hello.

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.

Thank you.

Timothy.

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- October 8th 2006, 02:57 PMTHulchenkoProof Question sequences
Hello.

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.

Thank you.

Timothy. - October 8th 2006, 04:03 PMPlato
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. - October 8th 2006, 04:57 PMThePerfectHacker