4. Define a sequence by an+1 = -an?, with -1 < ao < 0. Prove that {an} is increasing and bounded above.

Q: true or false: if the sequence [a sub(n)] is monotone decreasing, then [a sub(n)] must converge

A: Follow next step

Q: -) Determine the first six terms of the sequence defined by t₁ = -5 and t = 3t-1 + 8. 5, 23, -61,…

A:

Q: The greatest lower bound for the sequence {2, 4, 8, 16, 32, 64, . } is

A:

Q: Let {an} be a real number sequence. Prove that                             {an}= {1+(1/2n)}…

A:

Q: 2) Show that the sequence defined recursively by 3 4 An aj = 5 аn+1 satisfies 2 < an < 5 and is…

A:

Q: 19. an = IN 2 τη

A: The sequence is given as an=12-n

Q: (-1)"n An n +1

A: We have to evaluate the limit of the sequence an=-1nnn+1.

Q: Let (2) be a bounded sequence. Prove that if (en) is monotonically decreasing then it con- verges to…

A: To prove that a bounded, monotonically decreasing sequence {xn​} converges to its infimum, we need…

Q: Prove that sequence {an}= {(-1)n} does not have a limit.

A: According to the given information it is required to show that {an}= {(-1)n} has no limit.

Q: Suppose ao, a1, a2,... is a sequence such that ao = a1 = 1 and forn2 1, an+1 = n(an+an-1). Find az =…

A:

Q: Is the sequence a, convergent or divergent? Exp n+1

A: The given sequence is

Q: A sequence that does not have any convergent subsequence

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

Q: Use forward differencing to determine which of the following sequences (an) is not a polynomial of…

A: degree 2

Q: Assume that the recursively defined sequence converges and find its limit. a, = - 12, an - 1 = /24 +…

A:

Q: Does the sequence whose nth term () 2 an n converge? If so, find lim,→ an -

A:

Q: Use the definition to prove that {(-

A:

Q: 1. Let a, = 1 and an+1 = 1+ 1+an (a) Find the first six terms of the sequence {an}. (b) Prove that…

A: As you asked multiple sub parts so I answered 1st three subpart.