QUESTION 14 14. Which of the following sequences is/are convergent? (-) n I. an = 4n2 II. an n² + 3 2n III. an = n2 (A) I only (В) II only (С) III only (D) I and II only (E) II and III only О (4) О (В) (E)

Q: 30. а, 2 1+ %3D - n

A:

Q: Find the n" term a, of a sequence whose first four terms are given. 9 10 11 -- -- 4' 8' 12' 16

A: Given:-84,-98,-1012,-1116,....

Q: Find the explicit formula of the following sequence. 8 (72, 24, 8, 3, ...} O a O b Oc - Od ƒ(n) = a₁…

A: Given sequence is 72, 24, 8, 83, ...

Q: 2. The Fibonacci sequence (fn) := 0, 1, 1, 2, 3, 5, 8, . is an example of a recursive sequence with…

A: a)

Q: 12. Prove the following facts about the Fibonacci sequence (Fn): (1) (Chapter 10, #26) E-1 F =…

A: Given, The Fibonacci sequence (Fn) Fn=Fn-1+Fn-2, where F0=0 & F1=1

Q: Do the following scquences {a„} converge or diverge? Justify your answers. (a) an = 3 (b) an –…

A: "Since you have posted a question with multiple suparts, we will solve  three subparts (d), (e) and…

Q: 1. (a) ( ) Let {an}nez, be a constant sequence. Show by definition that {an} is convergent.

A:

Q: What is the point of the formula n. 2k in Example 1 of Section 11? For example, what does ng 16…

A:

Q: Let an be a sequence defined by a1 = 0 and a2 = 1 and for n > 3 an = (n – 1)(an-1+an-2). %3D

A: Here, the terms given in the series are, a1=0,a2=1an=n-1an-1+an-2 Calculate the third, forth and…

Q: 4. Consider the sequence Onvergent, to what? 3n+7 Determine whether this sequence is convergent or…

A: Sequence and it's convergence

Q: {dn} = SA { (. (₁₁²³²7) - (₁~^²+₁ ) ) ²^ } - (ⓇP) :)

A: The given sequence is defined by the formuladn=15((1+52)n−(1−52)n) We can find the first five terms…

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.