3) For which a does > Σ 1 converge? Justify your answer. n(In n)a n=2

Q: Determine the given below serie is converge conditionally, absolutely converge or diverge 4n° + 4 8n…

A:

Q: 3* + 4* 2) What does converge to?

A: ∑k=1∞3k+4k5k

Q: Determine whether the given converges or diverges. n Σ 2n + 1 n=1

A: Given is a series ∑n=1∞n2n+1n To check if the given series is convergent or divergent Ratio test:…

Q: an Q4. If £ an converges and an > 0 for all n , can anything be said about E- ?

A: Given that ∑an converges and an>0 for all n. The objective is to determine whether ∑1an converges…

Q: 2* converge? If so, what does it converge to? If not, justify. 7k 1 2 2. Does

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

A: The given series is

Q: Find all numbers x such that the series n=1 converges!

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Q: If E lan| converges then Ean converges. Select one: O True O False

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Q: What are all of the values of x such that (-1)"+1 Σ (3)" converges?

A: The ratio test states that: if L &lt; 1 then the series converges absolutely; if L &gt; 1 then the…

Q: (b) Use the comparison test to determine if the following improper converges: 5/T +1 7+x + x²

A: According to the given information it is required to check for the convergence: ∫1∞5x+17+x+x2dx

Q: If C.)" converges, then C,)" converges. n=0 n=0 Select one: True False

A:

Q: What are all of the values of x ,such that - (-1) n+A converges? n=1 .1 X26 .2 06

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Q: Find Sn for the serks n= Does the seres converge ?

A: Consider the given series. Sn=∑n=1∞1n+3-1n+4 Expend the series and find the limit…

Q: If 2 a, converges, then la,| diverges. n=1 n=1 True False

A: Given statement is FALSE. I HAVE given a counter -example.

Q: Σ Show that n2 + 1 converges/diverges n

A: The given series is: ∑n=1∞nn2+1 Let  an=nn2+1,n≥1    =nn21+1n2   =1n1+1n2 And, bn=1n

Q: If an| converges then diverges because for large n. Vn n=1 True False Reset Selection

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Q: Determine whether the given converges or diverges. n 2n +1 n=1

A: We can solve this as follows:

Q: What are all of the values of x ,such that Σ.. (-1)" + 1 converges? (31)"

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Q: If 0< by <1 for all k and , br converges, then , converges. Lk-1 %3D1 Select one: True O b. None of…

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Q: 2 n 1 o Show that + converges/diverges n-

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Q: 22n Σ n! n=1

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Q: (-1)" In(n) Vn n=2

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Q: 1 7. Determine by the ratio test if n- converges or diverges. п! -

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Q: + 4* 2) What does converge to?

A:

Q: 2. Find the interval of convergence of En=1 n(n+1)

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Q: 1/n 72,

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Q: 1 'n² – n-6 n=4

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Q: . Use the inegral test to show that =1 converges. 1+n2

A: To solve this question first we check derivative of function is negative for n&gt;0 and then we show…

Q: Use the Raho Test to determine whether thc serics is convergen Or divergent oo(-3 n 0

A: Here, the general term of series  an is shown on board. Forstly, we calculate next term and…

Q: Suppose that p(æ) > anx" converges on (-1, 1], find the internal of convergence of p(6x – 9). n=0

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Q: By limit comparison test, O None of these O converges O converges and diverges O diverges

A:

Q: Help please

A: Consider the given series:

Q: M Z(1-nsin-) converges n = 1 Select one: O True False

A:

Q: Let (rn) be a sequence of real numbers. Show that the convergence of (sn) implies theconvergence of…

A: We have to prove that if convergence of (sn) implies the convergence of (|sn|).

Q: 27 n! n=0 converges to 0. 8.

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Q: n+ 7) ) Σ n2 n=1

A:

Q: The sequence (-1)n+1 In=1 converge to is (i) Converge (ii) Diverge

A: The given sequence (-1)n+1n=1∞

Q: (1) Show that n2 +1 n=1 converges conditionally. Show that all conditions of the test used are…

A:

Q: 10. Define what it means for > an to be conditionally convergent and for b, to be absolutely n=1 n=1…

A:

Q: Use the Direct Comparison Test to determine the convergence or divergence of the s 5n Σ 4n - 1 n = 1…

A: Given query is to find series converges or diverges.

Q: Use comparison test to show that the series E=1 (2) converges. 5n2-п.

A:

Q: 8. Suppose ar > 0 and Does > ak converge or k diverge? Why? %3D

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Q: Find the values of p such that E(-1)"- converges.

A: The given series :

Q: Show that n* 3-" converges for all exponents k. n=1

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Q: The sequence (-1)n+10 In=1 is converge to (i) Converge (ii) Diverge

A: aur objectives to check the convergence.

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

A:

Q: 10. Define what it means for a, to be conditionally convergent and for b, to be absolutely n=1 n=1…

A: A series ∑n=1∞an said to be conditionally convergent series if the series ∑n=1∞an converges but the…

Q: 5. Use one of your comparison tests to decide if Σ n+1 converges. Justify your n° – 2n² – 7 n=3…

A: The given series is ∑n=3∞n+1n6-2n2-7