A sequence is said to be decreasing sequence if Vn > 1 'n+1°n =S .a .b O n+1 2n.cO n+1 n+1d0 n

Q: Compute the limits of the sequences sin (n² – 3n + 7) n² +1 | 2n? +п -5 (b) b, (c) c, = n°e (а) а,…

A:

Q: Which of the following information is correct for the sequence 2 8 1 dx 1 dx 1 dx 1 dx {an}n=l 4J x…

A:

Q: a) For what values of r> 0, the series "(sin n + cos n) converges. Justify your answer. b) Evaluate:…

A:

Q: The series elnz) - e) converge to n=1 (a)Ve - 1 (b) e - et (c)Ve - e3

A:

Q: Let S > a, be an infinite series such that SN = 9 – 6 n=1 10 16 (a) What are the values of an and >…

A:

Q: Solve the second order difference equation z(n + 2) + 4z(n + 1) – 21r(n) = 26(n) for 1(0) = 0 and…

A: Given second order difference equation is xn+2+4xn+1-21xn=2δnand x0=0 and x1=0

Q: The series 2 ÷, n =0 x" |x| >1 has a sum equal to: Select one: а. х b. х— 1 C. 1 1-x d. 1 х —1

A:

Q: A sequence S, is said to be bounded above if there is some number N such that Sn+12.a O Sn=N.cO S,…

A: Bounded above: A sequence an is said to be bounded above if there exists a real number M such that…

Q: Given that m is a positive integer and {D„} be the sequence with D = m and (Dn-1 + Dn-1 m D, = ,n >…

A:

Q: Find the sum of the series: E [ran-"(2n +1) – tan-(2n – 1)] n=1

A:

Q: 3. Find the exact value of the series S = > n(n +2)* n=1

A:

Q: For each of the sequences below, enter either diverges if the sequence diverges, or the limit of the…

A:

Q: Q4. If E a, converges and a, > 0 for all n, can anything be said about E2

A: Given that an is a positive term series and series an is convergent.   Here objective is to find…

Q: The series E cos(-) n =1 Select one: O a. converges to 1 O b. converges to Tt c. converges to 0 d.…

A: See the details solution in below

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

A:

Q: Write a formula for the nth term an of the sequence and determine its limit (if it exists). It is…

A: Given : 1) ln21,ln32,ln43,...ii) 0.9, 0.99, 0.999,....iii) 1, -14,19, -116,...v) cosπ, cosπ2,…

Q: defined in each item. Then, give its associated series 1. {4 – 2n} 2. ((-1)"(Зп — 2)} 3. {n? + 3п +…

A: Here we have to find the first five terms of the sequence whose general term is defined in each…

Q: Ś Co.q)" + CO.2)" n=0

A:

Q: Which of the following information is correct for the sequence 2 dx 1 4 dx 1 6. dx 1 8 1 dx {an}n=1…

A: We have to find the correct information for the sequence.…

Q: Given the power series 00 2 A x(n + 3) n = 0 1. Force the Exponent "n + 3" to be "R" like we did in…

A:

Q: Evaluate the limit of the sequence or state that it does not exist. an = ((3n2 + 2n + 1)sin n)/(4n3…

A:

Q: Let series c,, be positive for all values of n and; fa+1 A. B. C. D. 025 B unlim aum 4 for n 21.…

A: Given recurrence relation cncn+1=4 for n≥1 and cn is positive for all n.…

Q: Which of the following information is correct for the sequence 3 dx 1 5 dx 1 7 1 dx 9 dx {an}n=1 ? 5…

A:

Q: Find the limit of the sequence an (cos n) %D 6"

A:

Q: For n 2 3, the series 2+4+6+..+ 4(n) can be equivalent to .. ...... OA. n? +3 B. n +1 C. 3n2 + 4 OD.…

A: 3.  2+4+6+...+4n is equivalent to the option (A).

Q: The interval of conver gent for the series (-1)*x* is: 4kk (a)[-4,4] (b)(-4,4] (c) [-4, 4) (d)(-4,4)…

A:

Q: Which of the following is the sum of the series 00 3 3 (n+1)2 n-1 Select one: O A. 3/4 O B. 1/3 O…

A: Given series, ∑n=1∞3n2-3n+12

Q: (A) Find the sum of the seriesE3?*10'-k k=1

A: According to our guidelines , we can answer only first question . Kindly re-post other questions .…

Q: n In(n) n=1 is this Series Con lerges for my12?

A:

Q: 2n The sum of the series is (Gn (n!). n=1 (a) 7e2/7 – 7 1 e2/7 7 (b) (c) e2/7 7 - (d) e²/7 – 1 1 (e)…

A: To find some of the series we have to convert it into some taylor series form

Q: A sequence Sn is siad to be bounded below if there is some number N such that .... .a .b Sn+ n +1 .C…

A: Consider the given information. Now, define bounded. A sequence an is said to be bounded if and only…

Q: If the partial sum of the series La, n = 1 6n° +5n2 3n° + 6n + 1" is given by Sx Which of the…

A:

Q: The nth term of the series Esn sin n=1

A: Given:∑n=1∞Sinnπ2To determine the nth term of the series

Q: Which one of the following .10 sequences converges to_0 An = tan'(n) An = 2 %3D An = 2 (In n)² V An…

A: Given: We have to check which one of the sequences converges to 0

Q: By writing the summation of the two power series E=3 (n– 2)(n+1)c,x"-3+ En=0 Cnx" = 0, we obtain:…

A: Please see the answer below.

Q: es the sequences converges or diverges ? (n sin") , (cos) ,(cos 3. 2

A: We will use Ratio test to test convergency

Q: For each of (a)-(d) give a sequence (rn) with the stated prop- erties. In each case, the sequence…

A: Example and illustrations.

Q: The series {y} is described by y =5+0.3y,-1 +ɛ + 0.9ɛ-1. Identify the specific ARIMA model. What is…

A:

Q: Σ a cos n! For any a> 0, the series n=1 [ Select ]

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

Q: For what values of x does the series E-1 n=1 x21+3 12² converge?

A:

Q: 6n The sequence dn V10 + 25n? 6 O A. Converges to 25 3 O B. Converges to 3 OC. diverges 6 O D.…

A:

Q: The sum of the series E ,(-k+1) is k-3 O None 4 O 4 2 3 co| m

A: Expand the series, Apply formula of infinite sum of geometric series

Q: ch of the following sequences. Always justify your ans 1+ncos(2m) sin n+ c - In с) а, d) а, 2n 3 n°

A:

Q: Which of the following information is correct for the sequence 4 6. 8. dx 1 dx 1 {an}n=1= dx ... 1 1…

A: Given a1 = 12∫12dxx= 12lnx12= 12ln(2)-ln(1)= ln(2)2a2 = 14∫14dxx= 14lnx14= 14ln(4)-ln(1)= ln(4)4a3 =…

Q: For what Values of B does the series E,- 2n = 2 converge ? n3D2

A: We have to find values such that given series is convergent.

Q: Given the power series Σ 2 3 A x" n =0 Use the technique that we covered in this lesson to force the…

A:

Q: write down detailed e− N-proofs  i) (√n+7)/(n+5) converges.  ii) (n2−3i)/(2n3+2i) converges

A: Follow the steps.

Q: 5n The sequence an = V15 + 64n? O A. Converges to O B. diverges 5 Oc. Converges to 64 5 OD.…

A: Calculate the limit limn→∞an which will show if the series is convergent or not. Now,…

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.