n+ 7) ) Σ n2 n=1

Q: E(- 1)"+1cos?n converges conditionally n=1 Select one: True False

A: We have to find whether the given statement is true or false.

Q: Which of the sequences {a,} converge and which diverge: n+(-1)" 1. a=

A:

Q: (2!)2 C)) (2n)! n=1

A:

Q: 11 +4 Perform a test to determine if Tx converges. 1 11 X' + 4 Does T converge or diverge? 9 1…

A:

Q: Σ n=1 nP +1 converges if ? O A. p> 2 O B. p22 Ocp>1 O D.p22

A:

Q: b] If (s) converges then (s,) converges.

A:

Q: Spow it the arics is absolutely convergent, conditionally convergent, or diverg ent. (using…

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Q: Discuss the Convergence a 2 e¹ M8 n=1 SH n

A:

Q: Use the Ratio Test to prove that  ∑ (2/3) (n-1) converges. n goes thru n=3 to ∞. Write step by…

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Q: Does the sequences converges or diverges ? A) . (1-)") .«1 +(-1)"), ((-1)". (n+3 2n3 \n+1, n3+1

A: SOLUTION-

Q: 11. Let b be a real number with b > 1. Determine whether > 1 converges or diverges. As part 1+ bk…

A:

Q: Determine whether En=1n converges or m%3D1 2n

A: Given: ∑n=1∞n2n

Q: Which of the following nfnite senes are convergent? Select all that apply. 100 100+50+25 +... %3D 2…

A:

Q: Which of the following statements is false? If E a, converges but E Ja, I does not converge, then a,…

A: Explanation of the answer is as follows

Q: Which of the sequences {a,} converge and which diverge: 1. a, = 2+ (0.1)" 2. а, 1+-

A: 1) an=2+0.1n We know that if -1<r<1 then limn→∞rn=0 So, limn→∞0.1n=0 Thus, limn→∞2+0.1n=2+0=2…

Q: Ean converges and an > 0 for all n , can anything be said about E? An

A: If ∑ an converges and an > 0 for all n then ∑ 1an  converges         Proof :…

Q: determine whetheer the fene Conditionally (Convergent,abtolutely onvergent or dirergent a . n= 5…

A: We have to find whether the sequence is convergent or divergent and to know whether it is absolutely…

Q: Suppose (an) is Cauchy and that for every k ∈ N, the interval (−1/k, 1/k) contains at least one term…

A: Given, an is Cauchy sequence, Let, ank∈-1k,1k ,∀k∈ℕ Then, ank1k , ∀k∈ℕ Let, ε>0 be arbitrary and…

Q: Select the answer choices that make the following statements TRUE. (-1)" [ Select ] a. n=1 (-1)" b.…

A:

Q: ODoes an In(n) – In(n + 4) converge or diverge?

A: For convergence test, apply limn→∞ on an

Q: 1 79. For which a does converge? n(In n)" n=2

A: Let the given series be - y = ∑n=2∞ 1nlnnuWe can write it as - y = ∫2∞ 1nlnnadn…

Q: 13. Determine whether ∞ Σ(-1)* k1/2 k=1 converges absolutely, converges conditionally, or diverges.

A: The given series,    ∑k=1∞-1kk12

Q: 8. n2 - 1 A)E n³ + 4. n=1

A: ∑i=1∞ai is said to be CONVERGENT if the sequence of partial sum results in a finite limit value for…

Q: b. Eel/n – el/n+1 n=1

A:

Q: n2 + 5n + 2 Determine whether converges abso- (1+ )" lutely, converges conditionally, or diverges.…

A:

Q: Use the root test to find the radius of convergenc n n Σ (m+-+²1) ² = xn 9n +4 n=1

A: Introduction: The radius of convergence of a energy collection is the diameter of the most important…

Q: 3 9 9 27 81 20'40'80' 160

A:

Q: 2 – 5n 11п-1 n=1

A: Use ratio test.

Q: (-4)"n 2) Determine if £∞ n=1 Absolutely converges, converges conditionally, or diverges.

A: Ratio Test: Let∑an be a series and L=limn→∞an+1anif L<1 the series is absolutely convergent…

Q: 00 n 2 Does the seriesE (- 1)"n²| | converge absolutely, converge conditionally, or diverge? 3 n= 1…

A: Consider the series ∑n=1∞−1nn223n We have to check whether the given series is converges absolutely,…

Q: Determine if the following scries converges/diverges: n+ 166 12 – 165 =13

A: We are asked to find the series is convergent or divegent

Q: 1 'n² – n-6 n=4

A:

Q: 00 00 Show that > n3 + 8n converges by using the Direct Comparison Test with En3. n=1 n=1

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Q: Determine whether b, converges or diverges. n=1 п +1 a. bị = 1, bat1 = (-1)"; Зп + 2 °л b. b, = 3,…

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Q: 42. Given that la converges, does In (n) 1-1 (n²+5) ² $-10 converge or diverge? A. Dive B. Cannoe…

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Q: 1 B) V27n2 13. n=1

A:

Q: Suppose (an) is Cauchy and that for every k ∈ N, the interval (−1/k, 1/k) contains at least one term…

A: Observe that the given condition says that 0 is a subsequential  limit of the sequence.

Q: Vn7 +n Vnº + n5 n=1

A: Let's find.

Q: Does it converge or diverge? Σ 2 + 2n' n=2

A: Given series is ∑n=2∞n2+2nn

Q: Determine if the following converge or diverge. Explain your answer: 00 Σ) 4n+1. In=1

A:

Q: Determine whether ∞∑n=1n√3 converges or diverges.

A: The given series is Now, the nth term of series is

Q: 1) Does EA+() 1 converge or diverge? k k (4)*+(+)"

A: this is converges

Q: Prove if ( a n ) converges, then ( | a n | ) converges.

A:

Q: (n!)³ (3n)! 321. n=1 8.

A: we have to solve using ratio test

Q: 00 Use the root test to determine whether > an converges, where an is as follows. n=1 k k-1 328. ak…

A: A detailed solution is given below

Q: Q6) Test the convergence of the following 3) Σ=1 (n!)" (nn)²

A:

Q: Which series below conditionally converges? (-1)*-1ek VR A) Ek=1 yo (-1)k k%3D1 k3 100 K) 2k=1…

A: From the given four series, determine which of them are conditionally convergent, that is,…

Q: write down detailed e− N-proofs  i) (√n+7)/(n+5) converges.  ii) (n2−3i)/(2n3+2i) converges

A: Follow the steps.