Thread: Limit Question

How to i prove this?

If Xn -> X and X > 0, prove that there exists a natural number K such that
X/2 < Xn < 2X

for all n in K. (In particular, Xn > 0 for all n in K.)

Originally Posted by guess

How to i prove this?

If Xn -> X and X > 0, prove that there exists a natural number K such that
X/2 < Xn < 2X

for all n in K. (In particular, Xn > 0 for all n in K.)

You observe that for large enough that




CB

The definition of "limit of a sequence" is " is the limit of the sequence if and only if for any , there exist N such that if n> N, then .

If X> 0 then so is X/2. Apply the definition of "limit of a sequence" with .

If then so that .