Jse the limit theorems to prove that the following sequences converge. 15n2 – 6 sin(2n + 1). bn n +1 n; n + 2 9n dn (n +8)!" An :- Cn = n – 5n2 - 1 n

Q: Prove that the sequence {sin n + cos n is bounded. =1

A: The given sequence is We have to prove that the sequence is bounded.

Q: 2n en

A: 1. The sequence given is, an=2nenn=1∞ Take the limits, limn→∞an=limn→∞2nen Apply L'hospital rule,…

Q: QI Prove directly from the definition that the following sequence converges. (-1)" +n+1 (CoN(n*) +…

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Q: 2. Assume that p > 1. (a) For all n> 1 prove that P-1 (n + 1)P (b) Prove that is convergent. NP <…

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Q: Which of the following sequence is divergent? 32n² n² + 1 sinh n sin n ° {2 (+)} {-3-} None of the…

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Q: 8. Give a closed form for the sum You may assume that Σk=1 k = n(n+1) 2 1x2+2x3+ ... k(k + 1) and…

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Q: Using Sandwich Theorem, the sequence 2 = 4 – - Cos2 n +1 n³ converges to 4 converges to 2 diverges…

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Q: K+1 – /K k=1 VK² - +K

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Q: Determine p and the radius of convergence of the sum Σ (n!)³²n² -x²n 2n (2n)! n=0

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Q: Two of the following statements are true. Which ones? 8 If Σen (*1- x0)" converges, then en (x-xo)"…

A: Note that first and last option of your questions are same.

Q: Find the following infinite TM & α) Σ ntl (-3) n+1 A-1 5" infinite sums. 2 b) Σ (2n+1)(2n+3) n=1

A: Step 1: Step 2: Step 3: Step 4:

Q: 00 n-1/2 6 + cos (n) A) diverges B) converges

A: Given series is: ∑n=1∞n-126+cos2n

Q: H.w.Which af the fallowing series converge or diverg 80 Ln n 2. (h+i)! hai 4- n+4

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Q: 3. Express 0.7 + 0.007 + 0.00007 + ... using sigma notation. A) Σ0.7)1001 B ) Σο0.7)100" C)…

A: By using the formula of geometric progression and Arithmetic progression we can solve this question.

Q: аn +1 Suppose that 1 as n → o. Find the radius of convergence. an n2n E an( – 36)"x²n n=1

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Q: Let an (2n³ + 1) sinn n² +1 (1) Does the sequence (2) Does the series n=1 n² + 1 (2n³ + 1) sinn n¹ +…

A: Here we have given a sequence  where,

Q: Use the appropriate error theorem to find the sequence bn in terms of N, such that +00 1 1 IE(-1)".…

A: Since you have asked multiple questions, we will solve the Question (i) for you. If youwant any…

Q: Which of the following statements are true? ³n² sin(n²) I. lim : 1. n→∞0 n+1 II. Let {an} be a…

A: As per the question we are given three different mathematical claims which we have to verify and…

Q: (a) Give an example of a nonconstant complex sequence that converges to 5 + 2i.

A: Note: Hi! Thank you for the question as per the honor code, we’ll answer the first question since…

Q: 4. Prove that 12 does not converge uniformly on S = [1,∞). Hint: Use Lemma 17.5 from Bartle and the…

A: let us consider the series by f_n(x) fn(x) =∑1∞x2n2 we have∑1∞x2n2≤1n2 limn→∞fn(x)=f(x)=0 This…

Q: Using Sandwich Theorem, the sequence 2 an = 4 – Cos n2 + 1 - O diverges O converges to 4 converges…

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Q: Prove the following sequences diverge. (-5)"т + 3 2 sin ( 10"T + 4 en +n? +n +11 (Ъ) » (* ) 2n n -

A: We use basic of sequence.

Q: 27 n + 191 The sequence tan 9 n + 169 n=1 O converges to 3 O converges to 6. O diverges converges to…

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Q: 103n2 – 8 - 1. Xn := 4n2 + 99n + 3 1i. Xn := -n + Vn² + 3n 3n? + 2n iii. Xn := 2n n=1 8.

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Q: Which of the following sequence is divergent? en {"} (-1)*+1 n s n² In+1 } {-3}

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Q: (-2)1+3n(n+1) Test the convergence of Ln=2' by ratio test. n251+n

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Q: x[n] is shown in the figure below. Sketch the sequences x₁ [n] and x₂ [n] specified as: x₁ [n] =…

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Q: hat' H(x)= I ñ* ,x>1. (±) **9e グニン (a) Show that the series Convi unit on [a, as) where a> (b) Shaw…

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Q: um the following: (pa-py-kak k=0

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Q: For the sequence an = n cos n n² +1

A: given a sequence

Q: etermine the convergence or divergence of ∞ ΣΕ n=1 (−1)n+1 3η

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Q: Mark all of the sequences that are monotonic. {sin(n²)}1 In(n) l n P (2) n=1 { n=1 [n² − 1] n² + 1…

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Q: Which of the following statements are true? Vn² sin(n²) 1. n+1 I. lim II. Let {an} be a convergent…

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Q: Q1: A- Find the limits of the following series (-1)" ܐ R=0 22 Στη Σ iv- 6 (2n-1X2n+)

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Q: -) {in(6n) 2 n=2 =) an = In(6n³ – 4) – ) {cos(nt)}0 n=0

A: e) an=ln6n3-4-ln3n3+5n2-7n+8 determine if the series is convergent or divergent? if convergent find…

Q: Use the definition of convergence to prove lim COS n 72-00 n²n+1 = 0 || -

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