Q1. Test the convergence and divergence of (n+1)! 1. Σ=o (n + + ²7/1) 2. En=1 3!n!3n 2=0 57 3. Σ=1 of the following: 3n сosní 4n-1 B 4. Ex-1(n)

Q: Prove that if {sn} converges to L and L > 0, then there exists a number N such that sn > 0 for…

A: Let sn be a convergent sequence and converges to L>0. We have to prove that sn>0.

Q: a. Σχy, i=1 b. Σ(x)(y) C. (Σ' (Σ'

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

Q: Apply the Ratio Test to determine convergence or divergence, or state that the Ratio Test is…

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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: 3. Determine which of the following series converge: (a) ( d) Σ 50 + 2n n= n=1 n O n (e) n=1 (2n2 –…

A: Please note that according to guidelines only first 3subparts is solved.

Q: 3. Assume the sequence of positive numbers (sn) increases monotonically to infinity. Prove that Sn+1…

A: Let Sn be a sequence of positive numbers sn increase monotonically to infinity. ⇒limn→∞sn=∞     ∵ sn…

Q: Determine the convergence or divergence of the following series 2 sin³ n n² -1

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

Q: 8. Investigate for convergence or divergence, and explain why (a) E) n=1 n (b) Š_n! 3n!–1 n=0 ( c)…

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Q: 2. Let f (n) n5+7 n 12 n6 Find interval of convergence and radius of n7+n6 n7+n6 convergence of the…

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Q: A. Using convolution to find L-¹ [(5+2)(5+4)]. B. Test the divergence of the following series 00 n

A: Note:- according to the company policy we can attempt only one question so please upload the next…

Q: a. Show that if two power series E-oa„x" and E-o b,x" are convergent and equal for all values of x…

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Q: 12. Determine Converges a) = cos(n) which of the following series. b) = 1=1 c) 32² d) [(+)² 7-1 3 n

A: Since you have posted a question with multiple sub-parts, we will solve first three sub parts for…

Q: 3. Show divergence or find the sum of the series -5 +32n 11" n3D2

A: Given: The series ∑n=2∞-5n+32n11n To determine: The divergence or sum of the series.

Q: Find the limit (as n → ∞) of the sequence an = In(2n² + 5) – In(5n² + 2), n > 1. %3D

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Q: Suppose that xo 22 and xn = 2 + √xn-1-2 for ne N. Use the Monotone Convergence Theorem to show that…

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Q: 13) Determine which test you would use to show convergence or divergence for the following infinite…

A: Explanation of the answer is as follows

Q: Which of the following series diverge? = N/W 2 K² +1 1. Z K=05K² +7 I. II. Ex-2(-1)*(x²+4) m. ΣΧ.…

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Q: Match each of the following with the correct statement. C stands for Convergent, D stands for…

A: Concept used: Divergence: When the values goes to -∞ or goes to ∞ that is it does not approach one…

Q: 13. (a) Express each of following sum in sigma notation 1 a) 1 + 2 + 113 +... + 1 20 b)…

A: As per our guidelines we can answer only 1 question so kindly repost the remaining questions…

Q: n x + 2 .? х — 1 5. What is the domain of convergence of infinite series 3n n=1 What is the value of…

A: we have to find the domain of convergence of the given series and also find the value of it at X=-1

Q: 2. (a) Show that k!n-k-1 = for n>0 and ka nonnegative integer. 5. e-nxxk dx

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Q: The domain of convergence of the series E-o n²(,)"i O a. Iz2 – 1| < 2 O b. Iz – 1| < v2 Oc. O. Iz –…

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Q: 4a. i) Σ.n+2. n=0 ∞ Find the radius and the interval of convergence for the following power series…

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Q: Determine the limit of the sequences (2 * n + 1)2 – (n – 1)2 an = (n + 1)2 – (n – 1)2 cos(42 * n3)…

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Q: 1. Test the convergence and divergence of 2. Σ (n+1)! 3!n!3n 6n² 6. Σ=1n3+1 7. Σ=0 210-√n n2+1+2 of…

A: Disclaimer: Since you have posted a question with multiple sub-parts, we will solve the first three…

Q: Q3) Express cos(x²) as a power series. а) 1. 2! + 6! 4! x10 + 3! x14 +. 7! b) 1– 5! c) 1– x5 x7 + 7!…

A: To express the function cos(x2) as a power series. Here, note that the power series of the function…

Q: Which one of the following series is divergent? 1 1 (A) E (B) E 2n + n + 1 n2 + Vn n=1 n=2 1 (C) E…

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Q: (30-2)" n=1 Which of the following is the interval of convergence of the series O a. (1/3,5/3) O b.…

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Q: 3. Determine which of the fol 2" (a) n=1 n! (d 1 (b) (e n=1 2n 3n n+1 (c) (E 3n n=1

A: Since you have posted multiple questions i can do first three subparts as per our company guidelines…

Q: Both of the following series converge by comparison to E= n=1 4n² 00 3 3 and 4n2 +7 2.4n? – 7 n=1…

A: Given two series are  ∑n=1∞34n2+7 and ∑n=1∞34n2-7

Q: Apply the Ratio Test to determine convergence or divergence, or state that the Ratio Test is…

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

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