Sn/2", l1/2". if n is a prime number otherwise. Let an Does Ea, converge? Give reasons for your answer.

Q: For which values of x does > n!x" converge? n=0

A: To Determine: for which value of x does converges? Given: we have a power series  ∑n=0∞n!xn…

Q: If 2n=1a, converges, and if a„ # 1 and a,n > 0 for all n, a. Show that E=1a, converges. b. Does…

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Q: a) Does f() -Σne" n=0 converge or diverge for r > 0? b) How do you know?

A: According to ratio test, if the limit L<1, then the series converges and if L>1, then the…

Q: I. Consider an = V4n² + 3n – 2n for n >1. 1. Determine if {an}-1 is convergent or divergent. 2. Is >…

A: Simplify the expression of an. Multiply and divide the given expression of an by 4n2+3n+2n to…

Q: What are all of the values of x ,such that Σ (3x)" (-1)"+ 00 converges? n=1

A: To solve this question we shall use root test for series.

Q: (-1)ªn n² + 1 mula converges to a value or diverges withou

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Q: Which one of the following methods always converges while finding the root of f(x)= 0.

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Q: m-1 -4 m3D1 converges.

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Q: If E C, (x – 5)" converges at x = 11 and diverges at x = 15, what can you say about: (a) the…

A: Find the value of R and proceed. Find the center as clearly here it is 5 and proceed just as shown…

Q: Are the following convergent or divergent? Show your work and state the reason 100 11) Ση n=0

A: The summation of n, n from 0 to 100.

Q: Suppose that dz converges. What can we conclude about the constant p? Op>1 Op Op< 3

A: Explanation of the answer is as follows

Q: Š V2n-5 n=1 n2- 3n +4

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Q: a) For which values of x does f(x) =E n=0 converge and for which values ofx does it diverge? b) When…

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Q: ? 4. Show that the sequence {fn}, where nx fn(x) = XER 1+n²x²⁹ is point-wise convergent but is not…

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Q: O Determine whether E=1 converges or diverges. n! 104n t.

A: To determine whether series converges or divergent.  Here by using ratio test we will determine…

Q: Does E In n converge? n/2 n=1

A: We have to solve given problem:

Q: The infinite series 2 converges to L. By the use of the ratio te n! the value of L will be...

A: Given that  The infinite series converges to L To find the value of L by using the ratio test.

Q: Are there any values of x for which E=1(1/nx) converges? Give reasons for your answer.

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Q: What are all of the values of x ,such that Σ.. (-1)" + 1 converges? (31)"

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Q: 5n – 1 8) Σ 7n n=1

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Q: Q9:S a)converges to 2 b)converges to 을 c)converges to - 2 d)diverges

A: Since  you have posted a multiple  question according to guildlines I will solve first  (Q9)…

Q: etermine and justify if ∞ In(x) k=2 (1+k) ³/2 converges or diverges.

A: given series ∑k=2∞ln(x)(1+k)3/2

Q: 3) For which a does converge? Justify your answer. n(ln n)ª n=2

A: as per our guidelines we are supposed to answer?️ only one question. Kindly repost other question as…

Q: For which values of p does £=1 converge? (1+eon)4p

A: Given: To explain the given statement as follows, .

Q: N 2N + 1 2) Show that converges/diverges. +

A: We have to show whether the series converges or diverges.

Q: Q 9) Does the series: ∞ ∑    1/4n-1 n=1   converge or​ diverge? Give a reason for your answer.…

A: Use series integral test.

Q: Vn +1- n –1 n=1

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Q: (-1)" In(n) Vn n=2

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Q: E (n!)² (K)! Fan what e is convergent ?

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Q: 3n 4. Use the ratio test to determine whether Σ converges. (n + 1)! n=1

A: use the ratio test for convergence of series.

Q: Find the radius of convergence for: (2n)!æ" n=1

A: We will use direct formula for Radius of convergence without using ratio test

Q: The series E=1 is convergent. 1+(" Select one: O True False

A: ∑n=1∞ 21+34n

Q: The sequence {G 3n+2 n=1 O None converges to e O diverges converges to Ve? converges to e3

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Q: Q 12.11 whot values of does this Seirics seines converge? n (in u) n=2

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Q: п? For which values of p does Ln3 + 1)P 00 converge? п: n=1

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Q: Find radius of convergence and interval for the following: 00 Σ 2n n=1

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Q: Which test to use and is it convergent/divergent? Σ 16n2 – 8n – 3 n=1 - -

A: Use the ratio test, L=limn→∞an+1an=limn→∞116n+12-8n+1-3116n2-8n-3=limn→∞16n2-8n-316n+12-8n+1-3

Q: Lütfen birini seçin: a.Converges absolutely b.None of them c.Converges conditionally d.eventually…

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Q: 10.Does 00 sin? (n) 2n n=1 converge or diverge? Use any method and give reasons for your answers.

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Q: Find the interval of convergence for Σ 5 k?xk+1 ek+1

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Q: n=1 3" 2n2 M.

A: We shall use elementary knowledge of Series and summations to answer this question. Note that…

Q: The sequence {C+1 In=2)"} N=1 converges to e² O None diverges converges to le converges to e³

A: The given sequence 3n+23n+1nn=1∞ The sequence can be written as follows:…

Q: Use comparison test to show that the series E=1 (2) converges. 5n2-п.

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Q: that converges to a function on R ii)show n х 1=0n!

A: For this, we will use the Ratio Test, which can be written for a series ∑n=0∞an as: limn→∞ an+1 an…

Q: If 2(-1)" a, is absolutely convergente the n=0 na, is divergente. Select one: O True O False

A: Topic:- sequence and series

Q: O Does Eo 2k+² e-k converge or diverge? If it converges find the sum. "k=1'

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Q: Let fn(x) be the following sequence (not series) of functions n2 fn(x) = (x2 + 7x + 6)n² +n

A: