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Q: (b) Let a1 = 1 and an+1 = lim, an- /am+2. Prove that a, is convergent and find %3D

A: The recursive relation represent a bounded above increasing sequence

Q: T F If {an} is convergent, then {|an|} is convergent.

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Q: +00 E Un where s, = u1+...+un Vn +1 n=1

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Q: 1 E(-1)"+1, ( n + 1 ) . 3η n=1

A: To find whether converges or diverges

Q: 1 dx (x + 1)2 -2

A: We have to determine whether  ∫-2o{1/(x+1)2 }dx  is convergent or divergent.  Let I =  ∫-2o{1/(x+1)2…

Q: la) 을 In ? n=2 16) n=2

A: The solution of given problem is given as follows :

Q: The sequence V(n + 5)(n + 7) – n} is A) Convergent to 0. B) Divergent. C) limn-»0 V (n + 5)(n + 7) –…

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Q: nst. . Decide whether the fo lowing is convergent In the con ver or ०१en1 ९ase ८a्रlवnee ५e 6+1)4"+…

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Q: 52n 5n +1 n=1

A: Given that:- ∑n=1∞52n5n+1To find:- chek whather the series is convergent or divergentSolution:-limit…

Q: /2n?

A: The given series is: ∑n=1∞(-1)n(-1)n2n2+5=∑n=1∞(-1)2nn2+5n2=∑n=1∞1n2+5n2

Q: fnd all xeR where -5x (x+) n=2 ナS is Convergent- +5

A: We have to find all x∈ℝ such that the series ∑n=2∞ -5xx+1nx+1n-1+5x+1n+5 is convergent. We know that…

Q: Represent the function as a power series f(x) = ) Σ (1 – 9æ)² n3D0 Co C1 = C2 C3= C4= Find the…

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Q: Š V2n-5 n=1 n2- 3n +4

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Q: If > an is convergent and ) b, is divergent, then > (am + bn) is divergent. n=1 n=1 Select one: True…

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Q: Which of the following are convergent or divergent? Show your work. 72 i. En=2 lnn ii. En=1 3 1+ Vn…

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Q: Determine whether or not the infinite series below converges.

A: The given series is

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

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Q: a) Show by example that E( an /b.) may diverge even thagh E an and E bn converge and no b, equals 0.

A: Since solve the first question for you. If youwant any specific question to be solved then please…

Q: Determine whether E=1(-1)"+1. 2n converges or diverges. If it converges, find the sum. 3n

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Q: -4 x d.r Determine if the integral converges? 2-9

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Q: Determine if the given is convergent or divergent. (x²+1)² n Zn=1 (n²+1)²

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Q: e-n E(-1)"+1 2. п(п + 1) n=1

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Q: Show that if $a_{n}>0$ and $\Sigma a_{n}$ is convergent, then $\Sigma \ln \left(1+a_{n}\right)$…

A: Here, we are given that an > 0 and series is convergent. We need to prove that: is convergent.…

Q: (In(n))" 00 Find the value(s) of a such that 2 is convergent T2 Answer:

A: Given that, ∑n=2∞lnnan By using the integral test, ∫2∞lnnandn It can be written as, ∫2∞1nlnnadn

Q: Given: a, = In(n+1) – In(n) for n E N Determine if the following is convergent or divergent. (a)…

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Q: Σ-). Vn? – 1 n=2 A. conditionally convergent B. absolutely convergent C. divergent

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Q: 9. Determine whether the following is convergent or divergent +(-1)"+1 n! 2n 2e

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Q: Σ Suppose that ax" converges to a function y such that y" – 2y' + y = 0 where y(0) = 0 and y'(0) =…

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Q: 9n + 2" 46. Prove the divergence of n=0

A: Given series  ∑n=0∞9n+2n5n where an=9n+2n5n.

Q: +00 El-1)» (" – n)" 2η n=1

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Q: Test the following sevies Por being convergent or divergent. n+3 s (-リt) (-1) n(nt1)

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Q: k+ln k > ak, where aj = and ak+1 ak k+10 %3D k=1

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Q: etermine whether the following is convergent or divergent and j

A: Given that,

Q: Determine whether E1(-1)" sin n3 is absolute convergent, conditionally convergent, or %=D1…

A: We have to find the series test

Q: (-1)h 7^ (n!)? 2? (an+3)! A)is diverget B)is absolutely convergent O is conditionally conveglat

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Q: Determine whether or not the infinite series below converges.

A: Here the given series is

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

A: a) Given an = 4n2+ 3n   -2n Rationalize (4n2+ 3n  - 2n) (  4n2+ 3n  +  2n) (  4n2+ 3n  +  2n) = (…

Q: +00 (e) Σ (-1)" (n+1) In(n+1) n=100

A: The given problem is to determine whether the given series is convergent or divergent. We can check…

Q: Determine whether the scries is absolutely convergent, conditionally convergent, or divergent. (a) E…

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Q: 00 2 Σ п(n + 4) n=1 In(n) 5. 7n n=1 4.

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Q: Σ 1. 4n n=1

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Q: +00 Inn E(-1)": n2 n=2

A: Solution

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: Given the expression an = V4n² + 3n – 2n for n > 1 Check whether this is convergent or divergent: an…

A: The given sequence is a an=Sqrt(4n2+3n) -2n.

Q: dx is convergent a) true b) false O b

A: The given integral is: ∫1∞1x2dx To find it is convergent or divergent. The integral is convergent if…

Q: Determine whether or not the infinite series below converges.

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Q: Find the limit of the sequence a, n! 1 1 e e Divergent

A: Answer and explanation is given below..

Q: SELEC A) converges B) diverges C) D)

A: The given series is: ∑n=2∞1n3-n

Q: cos" (;) is absolutely convergent, conditionally convergent, or divergent. en?

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