3n The two convergent subsequences of the sequence (-1)+2 is

Q: A decreasing sequence where cn is greater than or equal to 1 for all n. If this sequence could…

A: A decreasing sequence where cn is greater than or equal to 1 for all n. That is, cn≥1, the sequence…

Q: (-1)"n For positive integer n, let an = 3" Determine whether the sequence {a,} is convergent.

A: Determine whether the sequence is convergent ?

Q: Show that any sequence of positive real numbers either has a subsequence that converges, or else a…

A: We have to show that any sequence of positive real numbers either has a subsequence that converges,…

Q: the sequence is converge or diverge?    an+(-1)n+1 / 2n-1

A: Let an=12n-1           Then the given series is in the form ∑n=1∞-1n+1an           Since…

Q: a1 =-1, an+1= An +6 An +2

A:

Q: If the sequence {a}, is convergent, then the sequence {x} defined by a₁+as+as++an-stan is also…

A:

Q: Find the limit of the sequence, or show why it doesn't exist, an = n4-(n8-n5)1/2.

A: Given,  Sequence                     an = n4-(n8-n5)1/2

Q: Find the conditions necessary for this sequence to be Cauchy. Хп xn+1 = axn+b 1 + xn

A: For the sequence (Xn)(Xn​) defined by the recurrence relation to be Cauchy, the condition necessary…

Q: Decide whether or not the infinite sequence is a cauchy sequence. If it is not a cauchy sequence,…

A:

Q: Every bounded sequence converges. True or False?

A: False

Q: determine whether the sequence is monotonic,whether it is bounded, and whether it converges. an =…

A: Given the sequence an=2n-13n. To determine whether the given sequence is monotonic, whether it is…

Q: A sequence that does not have any convergent subsequence

A: We find a sequence that does not have any convergent subsequence.

Q: Consider the recursive sequence a ÷(:+*) with a , =3. If I<a,<5 then A. The sequence (a ) is…

A:

Q: 2n Using the definition of a convergent sequence, prove lim n-00 3n+1 3

A: Suppose limn→∞2n3n+1=13 then for a given ε&gt;0 , there exist a natural number  N=N(ε)  such that…

Q: ∞ If the radius of convergence of the series Σ unx" is R then the radius of n=1 of the series un x²n…

A:

Q: Give the definition of a subsequence of a sequence Xn.

A: the definition of a subsequence of a sequence Xn.

Q: Assume that the recursively defined sequence converges and find its limit. 24 + 2an - 12, an+ a₁ = =…

A:

Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence.  It was invented by German mathematician Carl Friedrich Gauss.