4. Show that the series " is Convergent, but the (-1) squence s not summable.

Q: 2. Use the Integral Test to determine if the series Σ (n + 2)/4 1 n=1 converges or diverges.

A:

Q: 5. Show, by the alternating series test, that the series converges: >(-1)"-1 sin n=1

A: 5. The given series ∑n=1∞(-1)n-1sin1n

Q: 49. n=1

A: We have to check

Q: (-10)^n/(5n+3)*8^n+1,

A:

Q: The series from 1 to infinity of 5/9+2^n.  Does this series converge or diverge?

A: Topic:- limit for convergence test

Q: Use an appropriate test to determine whether the series converges. Σ k=1

A: Given series is ∑k=1∞7k+6-k. Then ak=7k+6-k (say). Let bk=1k. Then…

Q: Determine how many terms of the following convergent series must be summed to be sure that the…

A:

Q: Determine whether the series converges. k=1

A: We use limit test to find convergence or divergence of given series. Follow 2nd step.

Q: 2. Show that the series is conditionally convergent. n=2 cos(nx) √n ln n

A: Solution of the problem as follows

Q: n2 2 n +7 n=1

A:

Q: Use an appropriate test to determine whether the series converges. 2(k!)4 9(4k)! Σ k=1 By the this…

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Q: Find re radics Of convergence of the power Series : n5h

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Q: 3. Use the Ratio Test to determine whether the series en! converges or diverges. State n=1 if the…

A: The solution is given as

Q: Use an appropriate test to determine whether the series converges. 00 k3 Σ k5 +5 k =1 By the this…

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Q: Show that the series converges.

A:

Q: Does the series from 1 to infinity of ((-1)^(k+1)/((k+1)!) converge absolutely or converge…

A:

Q: 6. Show whether the series is convergent or divergent. Σ in! n=0

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Q: Does the series from 1 to  infinity of (n^2)e^(-n^3) converge or diverge?

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Q: Show that the series n" n' is convergent. Deduce that lim (2n)! (2n)! n=1

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Q: (7) Use the definition of convergence for a series to prove that 2 n2 + 4n + 3 n=0 converges. Find…

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Q: Does the series from 1 to infinity of ((-1)^k)/(k^(2/3)) converge absolutely or converge…

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Q: The series from n=1 to infinity of (-1)^n/(n!) is given.  Does this sum converge absolutely, or does…

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Q: 17. Explain why the series Eo converges. Which con- vergence tests could be used to prove this?

A:

Q: 3. Use the Integral Test to determine whether the series >ne-"" converges or diverges. n=1…

A: As per bartleby guidelines, for more than one questions, first needs to be solved and others are…

Q: 5) Justify whether the series is absolutely convergent, conditionally convergent, or divergent. 8.…

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Q: The series E,= is convergent. Select one: O True O False

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Q: I need help determining if the series (-1)k times (1/radical (k-1)) from k=2 to infinity, absolutely…

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Q: If the series an , and E (an + b,) are convergent series then b, may be a divergent series. Select…

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Q: (7) Use the definition of convergence for a series to prove that 2 Σ n2 + 4n + 3 n=0 converges. Find…

A: Solution :-

Q: In n is convergent or divergent Use the integral test to determine whether the series,

A:

Q: Does the series from 1 to  infinity of ((5n^3+n^2-15)/(n^3+2))^n converge or diverge by the root…

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Q: Show that the series whose nth term is n2 An 2n - 1 is convergent.

A:

Q: (c) One of these series converges absolutely. Which one? Compute its sum.

A:

Q: Q₁: Classify the following infinite Series to diverage and converge хо n! (Inn) In (Inn) и=3

A: Follow the steps.

Q: Apply the root test to prove that this series converges absolutely: (- 1)"*' 2" n=1

A: Ratio Testlimn→∞|an|n=LIf L<1,then absolutely convergent.If L>1 ,then Divergent.If L=1 then no…

Q: Suppose we also know that 1> an 0. and a converge. Then the series£ converge Select one: True False

A: By comparison test,

Q: How do we know the series is clearly conditionally convergent in a)?

A:

Q: Find the values of the convergent series   [From n=3 to infinity] E(-1/3)^3n *that E is the sum…

A: The series can be expressed as follows.

Q: 3. Suppose that the following alternating series converges. (-1)" n2" Determine the number values…

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Q: The series from n=1 to infinity of (16^n/2 ) / (2^2n), does this series converge or diverge.

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Q: Determine whether the series converges absolutely, conditionally, or diverges.

A:

Q: n+1 2n=1 n(n+2)

A:

Q: assume that |an+1/an| converges to ρ = 1/3 . What can you say about the convergence of the given…

A: The given series an is convergent.   Consider the series where all the terms of the series are non…

Q: Does the series from 1 to infinity of ((-1)^(k+1))/((k+1)!) converge conditionally or converge…

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Q: Does the series from k=1 to infiniity of sink/(k^2) converge absolutely, converge conditionally or…

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Q: .6. Determine which of the following series converge absolutely, converge conditionally or which…

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Q: Does the series from 1 to infinity of ((k!)^2/(2k)!)^k converge or diverge using the root test?

A: ROOT TEST

Q: Does the series from 1 to infinity of (n^2-1)/(n^2+n) converge or diverge?

A: Given series

Q: 32n +1 +00 n 5"–1

A: Determine the an and an+1 terms. an=32n+1n⋅5n−1an+1=32nn+1+1n⋅5n+1−1=32n2+2n+1n⋅5n

Q: Find the sum of the convergent series.

A: Given series : ∑n=0∞ -15n The given series is ∑n=0∞ -15n=1-15+125-1125+...... The given series is…