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.)
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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 .
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