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What else can I help you with?
What is Example of bounded sequence which is not Cauchy sequence?
((-1)^n)
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 are examples of convergent boundaries?
A convergent boundary is a deforming region where two tectonic plates or fragments move toward each other and collide. Some examples are; the forming of the Himalayas, New Zealand, and the Aleutian Islands.
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.
Is it true when a sequence is divergent then its subsequences are divergent explain?
Not always true. Eg the divergent series 1,0,2,0,3,0,4,... has both convergent and divergent sub-sequences.
Every uniformly convergent sequence of bounded function is uniformly bounded?
The answer is yes is and only if da limit of the sequence is a bounded function.The suficiency derives directly from the definition of the uniform convergence. The necesity follows from making n tend to infinity in |fn(x)|
What is Example of bounded sequence which is not Cauchy sequence?
((-1)^n)
How do you prove that the sum of a convergent sequence divided by n will converge?
You can use the comparison test. Since the convergent sequence divided by n is less that the convergent sequence, it must converge.
Prove that if a real sequence is bounded and monotone it converges?
A bounded and monotone sequence must converge due to the Monotone Convergence Theorem. If the sequence is monotonically increasing and bounded above, it approaches a least upper bound (supremum), while if it is monotonically decreasing and bounded below, it approaches a greatest lower bound (infimum). In either case, the sequence will converge to its supremum or infimum, respectively, demonstrating that any bounded monotone sequence converges.
A convergent sequence has a LUB or a what?
JUB
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.
Show that convergent sequence is bounded?
Wrong answer above. A limit is not the same thing as a limit point. A limit of a sequence is a limit point but not vice versa. Every bounded sequence does have at least one limit point. This is one of the versions of the Bolzano-Weierstrass theorem for sequences. The sequence {(-1)^n} actually has two limit points, -1 and 1, but no limit.
Any convergent sequence is a Cauchy sequence is converse true?
no converse is not true
What are components and examples of linear bounded automata?
it is an acceptor language.it bounded with both ends
What is a sequence which is not convergent defined as?
It could be divergent eg 1+1+1+1+... Or, it could be oscillating eg 1-1+1-1+ ... So there is no definition for a sequence that is not convergent except non-convergent.
Are the major lithospheric plates bounded by diverging and converging boundaries?
They are divided by divergent, convergent AND transform boundaries.
Is the limit exists for a monotone sequence An?
If a monotone sequence An is convergent, then a limit exists for it. On the other hand, if the sequence is divergent, then a limit does not exist.
