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Earn +20 ptsQ: What is Example of bounded sequence which is not Cauchy sequence?
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Is every cauchy sequence is convergent?
Every convergent sequence is Cauchy. Every Cauchy sequence in Rk is convergent, but this is not true in general, for example within S= {x:x€R, x>0} the Cauchy sequence (1/n) has no limit in s since 0 is not a member of S.
What Show that 1/2n is a cauchy sequence?
0.5
Prove that every convergent sequence is a Cauchy sequence?
The limits on an as n goes to infinity is aThen for some epsilon greater than 0, chose N such that for n>Nwe have |an-a| < epsilon.Now if m and n are > N we have |an-am|=|(am -a)-(an -a)|< or= |am -an | which is < or equal to 2 epsilor so the sequence is Cauchy.
Examples of bounded and not convergent sequence?
(0,1,0,1,...)
What is an example for sequence?
2,4,8,16,32,64,128....
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