Find the limit for the following sequences and determine their convergence: In n (-4)" n! i) an = ii) an = iii) ann-√√n²-1 T n /n

Q: nx (a): Show that the sequences is not uniformly convergent [0, 00]. on '1-n²x2

A: Given the sequence of function fnx=nx1-n2x2, x∈[0,∞) Now , for x=0, the sequence is 0,0,0,.... this…

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: a Let (n) be a constant sequence in R (i.e. there is some constant c such that In = c for all n).…

A:

Q: Determine whether the sequence converges or diverges. If it converges, find the limit. (2n-1)!] a)…

A:

Q: 4. (an)nen with an = n sin- 2n sin(2n) 5. (an)nen Wwith an = Vn 6. (an)nen With an = Vn2 + n-n 7.…

A: See the attachment

Q: Inn (а) аn 2 (6) а, — nsin (n = 1, 2, 3, . ) %3D - n +1'

A:

Q: Q1:- (A) Discuss the convergence of the given sequence : a(n) = cosh ln(n) (B) Evaluate: f dxdy…

A:

Q: Which of the following sequences is convergent? Select one: O a. lim, v00 n² +1 3n /n15 n2 cos(1/n)…

A: b

Q: / Find the limits of the following sequences and determine their convergence? an = n(1-cos — )

A: here I am using expension of function and then find the limits.

Q: Assume that the following sequence has a limit L. Find the value of L. 41/3, (4(4/3))\/3,…

A:

Q: For each of the following SEQUENCES, select whether they converge or diverge; for each that…

A: Disclaimer:  Since you have posted a question with multiple sub-parts, we will solve first three…

Q: Find the limit for the following sequences and determine their convergence (-4)" In n i) a, ii) a =…

A:

Q: 1. Is the sequence bounded, monotone, and convergent or divergent? If it is convergent, find the…

A:

Q: Analyse the convergence of the sequence {fn} where fu(x) = on R. 1+ na²

A:

Q: (b) Why? ) Consider the sequence {an = (-1)"}n€Z+· Is it divergent or convergent?

A:

Q: 1. Prove the sequence {a,} = (1 +-)" Converges to the limit e*, what about the sequence {b,} = (1…

A:

Q: 2. Determine the convergence and divergence of the following Sequences: 3" 6" b. (1 -)") c. flan a.…

A: Note : Our guidelines we are supposed to answer only first three subpart . Kindly repost other…

Q: I. Graph and evaluate the following sequences: Divergent or convergent, bounded or unbounded,…

A: We’ll answer the first question since the exact one wasn’tspecified. Please submit a new question…

Q: Investigate the following sequences. Determine whether they converge, and if so, determine their…

A:

Q: 2.Determine whether the following sequences converges or diverges a) (am.) = ( n! (2n + 1) (n + 1)!…

A: Given,

Q: I. Graph and evaluate the following sequences: Divergent or convergent, bounded or unbounded,…

A: Note: Every function f: N→Y ( where N is the set of natural numbers and for some space Y) is…

Q: Find the radius, the interval of convergence, and the sum: 2n x² n! Σ(1)". n=1

A: Let ∑n=0∞an(x−a)n be a infinite series,  then the interval of convergence is given by |x-a|<R ,…

Q: Consider the recursively defined sequence s1 = 1 and sn+1 = 1 / (3-sn) for n  ≥1. i. Prove that sn…

A: Consider the given sequence:

Q: I. Graph and evaluate the following sequences: Divergent or convergent, bounded or unbounded,…

A: From below figure, it is observed that the sequence an is bounded by 1 and –1. Also it is having…

Q: W: Which of the sequences {a,} ca 1. a, = 2+(0.1)"

A: Note- Since you have asked multiple questions, we will solve the first question for you. If you want…

Q: Vhich one of the following sequences does converge to 0? Зп +1 a. an = Зп — 1 O b. An=tan n n! O c.…

A:

Q: a) Find the general term an:? b) Write convergent if the sequence is convergent, divergent if…

A: Given: a) To find the general term  an