, Find the limit of this sequence, or else prove that the sequence diverges: (1- 3 In n an =

Q: Let (Sn) be convergent sequence, and suppose lim s, > a. Prove there exists a number N such that n>…

A: Given sn is a convergent sequence, and suppose limn→∞sn>a. Since sn is a convergent sequence,…

Q: If ( a n) is a sequence that diverges to ∞, prove that Iim n --> ∞ (1/a n) = 0

A: Assume that the sequence an diverges to ∞. That implies, limn→∞an=∞.

Q: Which of the sequences whose nth terms appear converge, and which diverge? Find the limit of each…

A: We find the limit of the an th term. limx→∞(an)=limx→∞1+(-1)nn=1+limx→∞(-1)nn=1+0=1

Q: Consider the following sequence: en + en (a) Show that the sequence is monotone and bounded (and…

A: Find the limit of the sequence

Q: Let p be a given Natural Number. Give a sequence (XN) that is not a Cauchy sequence, but it…

A:

Q: Which of the sequences {an} converge, andwhich diverge? Find the limit of each convergent sequence.…

A:

Q: Let (x,) be a convergent sequence of real numbers and let (a,) and (b,) be subsequences of (x,) with…

A:

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.