Which of the following sequences is strictly decreasing {-1)" } }", 8. O None n+ 1 S_n In+1 S 1

Q: A. Is the following sequence In n bounded above? an 2n B. If yes, what is it bounded by? If not,…

A: Here, the given sequence is {an} with an=ln n2n 1) Since ln n<2n the sequence is bounded above.

Q: 1 The sequence converges to - 2 /n² – 1 – /n² + n 20 Select one: True O False

A: The sequence 1n2-1-n2+n   converges to -2    we have to check it is true or false.

Q: 3. n-3n+5 n7 Sn=1

A:

Q: (1) Show that the series n+1 n -1 and n3 +1 n=2 converge. Be very clear about the steps you are…

A:

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

A: given,       a.     an=n!2n+1n+1!    ,  n∈Nb.    an=1n+1-n  ,   n∈N

Q: Q4] Show that the sequence (xn) = (T") for all n EN is not a Cauchy .sequence

A: A sequence {Xn}of real numbers is called a Cauchy sequence if for every positive real number ε,…

Q: The series (n+3) converge to n=1

A: by expanding the series we can find out the sum

Q: Which one of the following sequences converges? n? O A (-1)", 7n +9 OA. n O B. (-1)" В. 9n +4 O…

A:

Q: One of the following sequences is divergent ( 2n en n=1 n? {(-1)" n² + 1 J n=1 {-1", 3n ) (-1)n. n2…

A:

Q: Determine the limit of the sequence a, = [In(n + 1)-in(n)] 1 e 1 in 2 1 4 e Divergent N O

A: Topic = Limits

Q: Which of the following sequences is strictly decreasing O None 1 n+ 3 S n=1 In+3 n=1

A: Given: 1n+3n=1∞

Q: One of the following sequences is divergent S 2n ] en n=1 3n (-1)" . n2 +7 ) n=2 None {8}=1 n2 -1)"…

A:

Q: Which of the following sequences is a convergent and increasing sequence with greatest lower bound…

A: Here, we need to find the sequences which are convergent and increasing with greatest lower bound 1.

Q: Which of the following sequences is a convergent and increasing sequence with greatest lower bound…

A:

Q: Which of the following sequences is strictly decreasing 1. 00 n+3 77-1 n+3 n=1 {(-1)", 11 n+2 }:…

A: Answer is mentioned below

Q: One of the following sequences is divergent S 2n l Ten In=1 3n ° 1)" n² +7. n=2 O None n- -1)" n² +…

A:

Q: Consider the sequence (an : n greater than/equal to 1) given by an=(-1)n/en for all n.  Is this…

A: The given sequence is a (n) = (–1)n/en. Check the sequence is monotone or not.

Q: 27. Which of the following sequences are Cauchy sequences? sin n (a) 2n Σ 1 (c) dn =£ (-1)*-1 (b) Cn…

A:

Q: Ean converges and an > 0 for all n , can anything be said about E? An

A: If ∑ an converges and an > 0 for all n then ∑ 1an  converges         Proof :…

Q: Which of the following sequences is strictly decreasing 00 In+2 n=1 n+2 J n=1 n + 1 O None

A: Decreasing sequence.

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

A: See the attachment

Q: Which of the following sequences is a convergent and increasing sequence with greatest lower bound…

A: a) ann=1∞=n2 1, 4, 9, 16,....... The sequence is divergent. b) ann=1∞=2n-1 1, 3, 5, 7,..... This…

Q: Find a closed form solution for the following recursive sequence: An = an-1+ 2" for n > 2 with the…

A:

Q: Show the following sequences do not converge. (b) Sn = (-1)"n

A:

Q: Which of the following sequences is a convergent and decreasing sequence with least upper bound 1?…

A: The objective is to find the convergent and decreasing sequence with least upper bound 1.

Q: Suppose that the sequence {an} converges to a   and that a>0. Show that there is an index N such…

A: Prove the following as follows.

Q: Which of the following sequences is a convergent and increasing sequence with greatest lower bound…

A:

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

A:

Q: Examine the increasing and decreasing of each of the following sequences, whether they are bounded…

A:

Q: Which of the following sequences are convergent? Select all that apply. □ {플} O {} O {In(n + 1) –…

A: (1) The given sequence is n!7n For any value of n, value of numerator will always be smaller than…

Q: Which of the following sequence is divergent? en {"} (-1)*+1 n s n² In+1 } {-3}

A:

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: 00 00 Show that > n3 + 8n converges by using the Direct Comparison Test with En3. n=1 n=1

A:

Q: Consider the following sequence: {a,) = {n – n²} Sn=1 Use an+1 - An to show that the given sequence…

A: Calculus   sequence

Q: One of the following sequences is divergent 3n (-1)" n2 + 7 n=2 n2 (-1) n2 +1 n=1 2n n=1 O None…

A: The infinite sum is said to be divergence when n→∞, the summation limn→∞an≠0 and limn→∞an does not…

Q: One of the following sequences is converges : tan 'n 100 S1 A? O {(-1)" S 5n2 +1100 31 n-3 O {(-1)".…

A:

Q: The following sequence 2357" An = e\ n! converges toe O converges to 1 converges to 0 diverges

A:

Q: Which of the following sequences are convergent sequences? Select all that apply. 7" O an n7 1 O an…

A: sequences are given, we have to find the convergent sequence

Q: Determine the convergence of the following sequences. {sech n} a.

A: We have to solve given Questions.

Q: 00 n³n² COS 5n³ +3, 1

A: See the answer below

Q: Which of the following sequences is strictly decreasing n+2 {(-1)"} n+1S -1 O None n+2

A:

Q: Which of the following sequences is strictly decreasing {(-1)"n+2 S n=1 00 n+ 3 n=1 O None n + 3 S…

A:

Q: What about the sequence an =16 + (10n2+1)/en for all n.  Is it monotone? Does it converge?  If so,…

A: Given a sequence witn nth term is shown belowA function is said to be monotonic if it is entirely…

Q: 1. Represent each of the following sequences by a formula, a, = f (n), with the given starting…

A:

Q: Which of the following sequences in R is convergent? (a) x_n= n + (3/n) - (b) x_n= −1 + ( [(-1)^n]/n…

A: keeping a note ?as per our company guidelines we are supposed to answer ?️only first 3 sub-parts.…

Q: Specify which of the following sequences converge n en bn n2 n + V5 an = 5 Cn = n an and bn the…

A: We have to check the following sequences converge or not ; (i) an = 5 - 1nn (ii) bn = enn2 (iii) cn…

Q: Which of the following sequences converge, and which diverge 2- an In(n²) %3D 3- an= 4-7n %3D 1- an…

A: (1). The given sequences is: an=n-2nn

Q: Which of the following sequences is strictly decreasing n+15 n-1 O None {(-1)"}}", 00 72 in+1 S-1

A: Sequence 1/(n+1) is strictly decreasing sequence

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.