an n=1 is absolutely convergent, then а, n=1

Q: 1 vn Vn + 1, n=16

A:

Q: Find the sum of the convergent series. 1 (n + 1)(n + 2)

A: To expand the summation, split the given summation into the summation of two series.…

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: la) 을 In ? n=2 16) n=2

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

Q: Find the sum of the convergent series.

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Q: 00 Show that converges if [r| < 1. п: п

A: The given series is

Q: Please determine whether each of the following is absolutely convergent, conditionally convergent or…

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Q: (e) Č(-1)"e Σ (-1)"e¯n

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Q: Does the series 1+1/2+1/3+1/4+1/5... converge or diverge? Explain

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Q: (-1)* Lk=3 In k absolutely convergent, conditionally convergent, or divergent? 100

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Q: Determine whether En=1n?e- converges or diverges.

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Q: The series 2=1 1 k is divergent no conclusion absolutely convergent conditionally convergent

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Q: 5n – 1 8) Σ 7n n=1

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Q: The series 1(-1)" converges to 0. True False

A: We have to find if the given series is converges.

Q: The series O True O False Σ (-1)^+1 n=2 n3+1 is absolutely convergent.

A: The given series is summation of (-1)n+1/(n3+1), n from 2 to infinity.

Q: e-n E(-1)"+1 2. п(п + 1) n=1

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Q: e-n n(n + 1) E(-1)"+1. n=l

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

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

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: If {fn}n=1 is a pointwise convergent, then {fn}=1 is uniformly convergent.

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Q: 1) (am) is not convergent but (a,(a, - 2)) is convergent.

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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: Find the sum of the convergent series. 2 [(0.9)" + (0.2)] n = 0

A: We have the given series as ∑n=0∞0.9n+0.2n Now, we have ∑n=0∞0.9n is a geometric series with a=1 and…

Q: , 2η En=1 3 er

A: Given series is ∑n=1∞ n2nen3. Here, an=n2nen3.

Q: 22n Σ n! n=1

A:

Q: 6 Let an 3n + 1 (a) Determine whether {a,} is convergent. convergent O divergent (b) Determine…

A: We can find the answer as below.

Q: The series True O False Σ n=1 (-1)"-3 √n is absolutely convergent.

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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: Find the smallest positive integer n so that S, approximates the sum of the convergent ser to four…

A: Here we have to find the smallest positive integer n so so the Sn, approximates the sum of the…

Q: If E Un is absolutely convergent then (un)² is also n=1 n=1 convergent.

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Q: The series 2(- 1)"+1 converges n = 1 Select one: True

A: The given series is ∑n=1∞-1n+1

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

A: ∑n=1∞ 21+34n

Q: Find the sum of the convergent series. Σ 4 5 n = 0

A: Sum if given convergent series is 45.

Q: ca, is convergent. is an convergent and c is a nonzero constant, then If n=1 n=1

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Q: If \( \{a_n\}\)  is decreasing and bounded below then it is convergent.  true or false?

A: Monotone Convergence Theorem : Every bounded monotone sequence is convergent.

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

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Q: Oiscuss the Convergen ce or Divergence n? tin3 n3 -1

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Q: (a) if Ek až is absolutely convergent then E ar is absolutely convergent.

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Q: 5) Does vergent? (-1)"n Ln=1 \n³+2 converge absolutely, converge conditionally, or di-

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Q: The series 2 1 is convergent. n =1 n(2) Select one: O True O False

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Q: If I want to show that >1 an is convergent, it would be appropriate to use the direct %=D1…

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Q: The series E "k 1 is ek 3D1 absolutely convergent divergent conditionally convergent no conclusion

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Q: 3k 5- 2k+1 k=1 2 1. Does converge? If so, what does it converge to? If not, justify.

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

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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…