Investigate the following sequences. Determine whether they converge, and if so, determine their limit. S+2 1 (an)neN with a, 2 (a,)ncn with a, = 1 (a,)meN With a, =| 4 (a,)ncN with a, = n sin . (a,)nes with a, = (uzjus 6 (a,)meN With a, = vn? + n-n 2. (a,)x With a. =+2+

Q: can anything be said about E- an

A: Given that, ∑nan converges.

Q: Which of the following is the limit 00 of the sequence {a,},where an = 3? 3 8

A: The objective of the question is choose the correct option.

Q: In Learning Exercises 3-10, find a possible function rule for each table. Then use vour m to find…

A:

Q: p) State Cauchy's Schwarz Inequality and prove this for Space of Continuous functions on[-n, n].

A:

Q: n+1 (-3)*1 3n n=1

A: Ratio test : Suppose we have a series ∑n=1∞ an then define  c=limn→∞ an+1an . If 0≤c<1 then the…

Q: Determine if converge or diverge using nth term and if converge find its limit

A: Finally, we can say that : The sequence an​=(−1)nn+1n​ diverges.The sequence an​=4n3n+n​​…

Q: Discuss the Convergence a 2 e¹ M8 n=1 SH n

A:

Q: 17. Let (Hn) be a sequence defined by Hn k' k=1 1 0, n +1 (b) Deduce that In(n + 1) < Hn < Inn+1…

A: Note: Since we can solve first three subparts of a question, we have solved the first three…

Q: The sequence shows the total number of rodents in an abandoned warehouse at the end of each month…

A: Given the sequence is 16, 24, 36, 54, 81,  …

Q: Find the limit if the sequence converges and lim sup and lim inf if the sequences diverges (c and d)

A:

Q: 50. A sequence a, is defined inductively as a, = v3 and a41 = /3 + a, ,Vn 2 1. Find the limit %3D of…

A:

Q: Use |S – SN| < bN +1 to find the smallest value of N such that Sy approximates the value of the sum…

A: According to the given information, it is required to find the smallest value of N such that SN…

Q: Suppose real sequences (sn) and (tn) are bounded. (That is, that their ranges are bounded sets.) i.…

A: Bounded sequence and sum of bounded sequences.

Q: (-1)" . 2n 4 – 5n (-1)" · 2

A:

Q: +9 for all n2 1. Prove that {r,} converges and find 2.1 4. (a) Let r = 4 and am+1 its limit.

A: Sometimes, a sequence is defined recursively. In that case, to test the convergence of the sequence,…

Q: Q.2) Determine of each point convergens or diverges: (-1)"(3n)!/ /n! (n + 1)! (n+ 2)!

A: determine whether the series converges of diverges (i) ∑n=0∞-1n3n!n!n+1!n+2! we will use ratio test…

Q: A sequence a, is defined inductively as a1 of an if an < an +1 Vn 2 1. A.글 (1± v13) B. (1– V13) C.…

A:

Q: On Saturday morning , it took Jennifer 3.6hrs to drive to her mother's house for the weekend. On…

A: Let we use the notationdistance = dspeed = sTime=t We know that  Distance=speed*time

Q: (5) Let' (1) : r² + 7x + 12. S(z) dr (a) Use a comparison test to show that. A B converges. S(x) (b)…

A: Introduction: An improper integration is an integration where the integrand is undefined in one of…

Q: of sequence Ex: Evaluate The DFT of (n) = [1,0,0,1] nyo 3

A:

Q: 5. Find the limit of the sequence 3. an ), n = 1,2, 3, --. 3JT

A: Explained below

Q: Which one of the following sequences does diverge to infinity? Oa. an Inn O b. an In 2n OC. 2n O d.…

A:

Q: (k + 1)/2 (k5 + k3 – 1)/3 1. Show that converges. k=1

A:

Q: ShipMaters finds that the numbers of orders it can fill per day when x people are employed at its…

A:

Q: 43. Which of these sequences is/are not bounded? I: a, 1= (-1)", n 21 A. III only B. I only C. II…

A:

Q: SntXn stx

A: We have to test the convergency.

Q: Which of the following sequences are bounded? Select all such sequences. X That's not right. 6n…

A:

Q: 26. The interval of convergence for (X-3)* k - (x– is а. (-3, 3] b. [-3, 3] с. (-2, 4) d. [2, 4] е.…

A:

Q: + inf 1 Σ п2 — Зп + 2 n=3 W

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.