4n The sequence an %3D 12 + 64n2 O A None of these O B. diverges 1 Oc. Converges to 16 1 O D. Converges to 2 OE. Converges to 1/3

Q: 2k k! - Decide if this series converges or diverges Lk=1 (k+2)!

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Q: For which values of x does the geometric series 2 2" x" converges? n D0 Select one: a. Ob. 12x >3…

A: Geometric series converges when |r| <1  Here r is common ratio

Q: Find all values of p for which the series converges. nP +3 n=1 (A) p> 5 (B) p3 (E) p<5

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

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Q: The series 2+ Vn2 1+ Vna n: is convergent if and only if: Select one: O a. 72 a d. 35 a 4

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Q: The series 1 + Vn? 1+ Vna 00 n=1 is convergent if and only if: Select one: 72 a > Ob. 35 a * 35 4 O…

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Q: Which of the following is the sum of the series n=1 n2+4n+3 if it converges? O a. 1/2 Ob. It is a…

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Q: 25. Choose the series that is convergent: ΑΣ A) 1+ n n+1 B ) Σ- 2 n n 4n n1 ο Σ7m 3 n n 2 D Σν+1 +4n…

A: In order to identify the convergence of series from given options, apply the divergence tests as…

Q: 12.The following geometric series : +00 2n+1 3n n=0 a. Is divergent b. Converges to 3 c. Converges…

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Q: Which of the following is the sum of the series0 Ln=1 +3n2+2n if it converges? O a. 1/2 O b. 0 O c.…

A: Break the given series in partial partial fraction then find their sum .

Q: 9).  For which p does the series ∞     n = 1 6pn 7n converge?   please show step by step .

A: This is a question of series.

Q: 00 The series - eln+3 converge to n=1 (a)Ve – 1 (b) e³ – e* (c)Ve – e3 (d) e² – 1 None

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

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Q: For what values of z does the series n²(¹3)" =1 converge? Find the sum.

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Q: (х-1)° converge absolutely? n° For which value(s) of x will the series n=1

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Q: In n Q10 ) The series E n n=1 3n-4, a) converges to 0 b) diverges c) converges by the root test d)…

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Q: Which of the following is the sum of the series 3 9 if it converges? 1 O a. 1/4 O b. 1/2 O c. 0 O d.…

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Q: The series 00 1 + Vn? 1 + Vna n=1 is convergent if and only if: Select one: Oa. 72 a > Ob. 35 a 4…

A: (.)   The given series is ,                                                        ∑n=1∞1+n281+na7…

Q: In The sequence an 2 W16+36n 7. OA Converges to 16 7. OB. Converges to 7. COC. Converges to 36 OD…

A: Let &lt;an&gt; be an sequence and let l∈R . The real number l is said to be limit of the sequence…

Q: -n 5n² – 2n + 1 00 - Determine whether the series converges or diverges. Show all your work. Зп? + п…

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Q: COS n 9. The series > n3 n=1 (a) converges absolutely. (b) converges conditionally. (c) diverges.

A: There are various tests to check the convergence of series. One of test is if a series converges…

Q: The series > diverges. 3n2 + n+1 n=1

A: We have to check

Q: n! The series E=1 is convergent

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Q: (-1)"(n+ 1)" Does the series converge absolutely, converge conditionally, or diverge? (2n)" n=1

A: We have to check convergence of given series.

Q: The series E(-1)"-1. Vn+1 is conditionally n=1 convergent, but not absolutely convergent. Select…

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Q: The sequence {Pn =}1 converges n-1 to p = 0 of order a = %3D O a. 3 O b. 1 О с. 2

A: For some number p, if the condition limn→∞an+1anp=M&gt;0 is satisfied, then the order of convergence…

Q: s the series n=1 _n+p diverges?

A: We have given an alternative series , we have to check the divergence of series

Q: 7 Q9) The series 2 n =1 (4n - 1)(4n +3) 7 a) converges to 12 7 b) converges to 18 7 c) converges to…

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Q: The series 00 14 2+ Vn2 1+ Vna n=1 is convergent if and only if: Select one: 144 a > а. b. a 4 d.…

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Q: , 4" – 3" 4. (a) If the series, E* 5" converges, what is its sum? H=0 (b) Does the series cos(n7)…

A: I am going to solve the given problem by first checking the convergence and divergence of the given…

Q: 3n+1 Σ 6n-1

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Q: k 5( – 1.2)“ is an alternating geometric series, which O divergesO converges. - k=0 E 5( – 1.2)* -…

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Q: •(-1)*x* 4kk k=1 terval of convergent for the series is: (a)[-4,4] (b)(-4, 4] (c) [-4, 4) (d)(-4,4)…

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Q: The series E n=0 converges to 2+/2 Select one: True O False

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Q: For what values of x does the series, x-6)+x-6} -x-6} + 1 (x-6)" ... converge? 16 64 Find the first…

A: Answer

Q: O The series Σ7-"[2 +5¹] n=1 converges to none of the choices the above converges to converges to…

A: The above series converges to

Q: The given power series : 4?n (x +3)" 9n n=0 is convergent if |(2x + 3)| <

A: We have to find the given series is convergent for which value

Q: Which of the following sequence is divergent? 3- 2n²\ n² + 1 S ( 3 sinh n sin n °{2(#)} 0{-3.} None…

A: Sol:- Check for Sequence Divergent Option :- First ∑n=0∞ 3-2n2n2+1Apply Series Divergence TestIf…

Q: n 3 The numerical series ) n' log .3 n3 n=3 O converges to a negative number. O diverges to-00.…

A: Using limit comparison test

Q: 1. Use the fact that E nxn-1 to find the sum of each series. (1 – x)2 n- 1 9 (a) 10 n- 1 10 11 n- 1…

A: Given,          Use the fact 11-x2=∑n=1∞nxn-1

Q: Find the sum (if it exists) of the infinite series ak, whose n" partial sum S, is k 1 calculated to…

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Q: E 2 > 2 ke-k converges or diverges Determine whether the series

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

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Q: Find the smallest value of x for which the series (エ+48)” 2!n(n) n=2 is conditionally convergent.

A: Given series is ∑n=2∞(x+48)n2ln(n)

Q: For which value of p the series 1 n=1 is divergent? 1/8 8 the series converges for all p>0

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Q: If dr converges, then which of the following must be true? Select one: a. Ln-1 n diverges. b. p<0…

A: We have to find the correct option.

Q: Which of the following is the sum of the series 1. if it converges? Ln=1 n³+3n² +2n O a. 1/8 O b. 0…

A: Here we have to find the sum of the given series.

Q: Evaluate the following and detemine if the sequence {a,} converges or diverges 5n2 + 9n 11 12n an 2n…

A: limn→∞an=limn→∞12n3-5n2+9n-112n3-3n2+7n+5=limn→∞n312-5n+9n2-11n3n32-3n+7n2+5n3=122=6

Q: Suppose E an has partial = an 21. n=1,2,3,.. Sums Does the series converge ? Find an fn n7a.…

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