The general term of sequence I,Ź stanting by n =D0 is

Q: Q1/ is the sequence {a,) converge > sin n

A: We have to find given sequence is convergent or not .

Q: For Exercise, find the sum of the geometric series, if possible. SU 10 Σ 3/2)1 n=1

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Q: By squeeze theorem, the sequence an= is n2 converges to, OA. 0 OB.1 Ов. Oc. D.

A: The given sequence lies between limn→∞cos-πn2 and limn→∞cosπn2.

Q: For the sequence (5) find the value of m E N , given that Ɛ = 2n %3| e 10

A: Given sequence an=12n, ε=1e10 Let n>m an-am=12n-12m=12m-12n  n>m⇒ 2n>2m⇒12m>12n…

Q: As n increases, the terms of the sequence: an = (1 + 1/n)n get closer and closer to the number e…

A: an=1+1nn We need to find a10,a100,a1,000,a10,000,a1,00,000  and compare these terms for the decimal…

Q: Calculate, to four decimal places, the first ten terms of the sequence and use them to plot the…

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Q: Write out the first few terms of the geometric series, > , to find a and r, and find the sum of the…

A: Given geometric series: ∑n=0∞3x-44n substituting n=0, 1, 2 , 3.. will give first term(a), second…

Q: The third term in the sequence with a=4 and a = a + 3n wheren>1 is %3D O 22 0 4 O 13 O 10 O 19

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Q: The limit of the sequence a, = (-1)"2 is equal to %3D Select one: True O False

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Q: For Exercise, find the sum of the geometric series, if possible. 4 J=1

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Q: The limit of the sequence z = Arg(-i+) is equal to

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Q: Not all sequences progress in the same way. You will need to use your imagination to find the nh…

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Q: Which of the following is true for the sequence, Vn? sin(n2) n3 +1 an = Converges to 0. o Converges…

A: Given sequence is  n32sin(n2)n3+1

Q: The radius of conver gent for the series is : (n+2)(n+1) n=1 (a)o (b)0 (d) 3 (e) None

A: To find the radius of convergence.

Q: A Sequence is defined by the recusire rule Cn= Cn-1 , with Ci = 5 %3D which of the falawng %3D…

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Q: Given the power series 2 5 A, x" n =0 Use the technique that we covered in this lesson to force the…

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Q: determine the number of term n in each geometric series ex:1 a1=-2, r=2, Sn=-14 ex2: a1=2, r=2,…

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Q: Use the equation editor or submit a picture of your justification Find the sum of the infinite…

A: We have to find out the sum

Q: Write out the first five terms of the sequence {n sin÷.. and decide if it converges. n=1

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Q: The formula for the sum of the first n terms of a geometric series is given by  Sn =_______(r ≠ 1).

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Q: Which of the options is correct for the following sequence: 4n

A: here last option is true because if be put n=1 than value is 1/4  and take limit at n->infinite…

Q: Assume "t*1*" represents the first term of a sequence and "t*n*" represents the nth term. What is…

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Q: We say that a sequence of real numbers (xn)nɛN converges to the real number а, if Ve > 0,3N E N, Vn…

A: Given sequence is xn=-1n+2-n. Definition: A sequence of real numbers xnn∈N converges to the real…

Q: If the third term in the geometric series Larn is -108 and the sixth term is 32 then the ratio of n…

A: We have to find the ratio of given geometric series.

Q: Find the limit of the sequence whose terms are given by 5 (n²) (1 – cos an

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Q: Suppose that the sequence (c,) converges to -1. Which of the following sequences converges to 2…

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Q: To what limit does the sequence S, 3+n converge as n approaches infinity? 3" %3D (A) 1 (B) 1 T. (C)…

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Q: The sum of the series 5 + is given by A. and 27 is given by B njo

A: sum of infinite geometric series:a+ar+ar2+····=a1-r where r<1-----i

Q: Find the z trans form of the casual sequence i Xx3 where XK = C-1). %3D

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Q: A sequence is said to be decreasing sequence if Vn 2 1 =DS n+1 aO .b O n+1 n+12s.cO 2n.d O n+1

A: Option (b) is correct.

Q: > The general term of the sequence 1, 2' 4 , starting by n=0 is .. +00 (i) n+1 +00 (ii) (iii)None of…

A: In the question it is asked to solve for the general term of the sequence given in question.

Q: The limit of the sequence z, = Arg(-i+) is equal to Select one: -T O a. O b. O c. -3T O d. 2

A: The correct option is option (a) - π/2    The detailed solution is as follows below:

Q: 2nt an tan 1+8n, n2 an Vn3+4n

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Q: The limit of the sequence Zn = Arg(-i+) is equal to Select one: -TO O a. O b. 21 -3T O d.

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Q: If t_n=3.5n+4.5, find t_1 ,t_10 and t_n+1-t_n. Is 85 a term of this sequence

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Q: Find the limit of the following sequence, using L'Hôpital's rule when appropriate. (n – 1)? (n + 1)2…

A: limn→0 (n-1)2(n+1)2=(0-1)2(0+1)2                    =1

Q: Let an be the nh element of the sequence 5,8,11.14,17,., then an.dxn+c for constant values d and c.…

A: What is d??

Q: Find the limit of the sequence a, (cos n) 2" =

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Q: Given the following sequence: 33, 30, 27, 24, ... [2] Write a formula to generate the nh term and be…

A: We have to solve

Q: You are given the sequence defined by a₁ = 4, a2 = 7 and for m≥ 3, am = am-1+am-2. Prove (using…

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Q: What would be the 31st term of the sequence x?,x, 1.. .... ..... .... A. x28 1 В. x26 1 C. x28 1 D.…

A: The solution are next step..

Q: Suppose you are given sequence dn that is described by a formula, and the starting index is 2. If…

A: a) -2

Q: dentify the sequence as geometric ór arithmetič. (r, = 11000 Im = 0.7rn-1

A: We can check the series as below by definition of geometric series

Q: Suppose that the sequence (b converges to 2. Which of the following sequences converges to 4…

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Q: et {B„} C R be a sequence and x € (0,1). Prove that if |B,+1– B,| 1 hen {B,} is Cauchy and hence…

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Q: Given the geometeric sequence 8, 6/1, 9/2 find an explicit formula for an

A: Let's call the i-th term of the sequence as ai.We have a1 = 8a2 = 6and a3 = 9/2

Q: 1) Using the appropriate formula, find the 17th lerm of the sequence 7,4, 1,......

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

Q: The limit of the sequence z, = Arg(-i+) is equal to 5. Select one: O a. -T 2 O b. -37 2 Oc. T 2 d.…

A: The limit of the sequence is, option (a) - π/2    The detailed solution is as follows below:

Q: 16. For what value of n is the following sequence A". If c = 2, find Co. %3D Cn = 2,4,10,23,46,82,…

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Q: ) For the sequence (÷) find the value of m E N, given that Ɛ = 2n 1 e10

A: Here, note that  limn→∞12n=0 And, the given ε=1e10, to find m such that 12n-0<ε whenever n>m

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.