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

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

A: Given that, ∑ an  converges We known that, the series if  ∑n = 1∞ an  is convergent then limn→∞ an =…

Q: Prove that following sequences converges to zero. 2n Xn n² + Tt

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

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Q: If (an) is a sequence converging to L, with an 20 for all n, prove that L≥ 0 and that (√an)1…

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

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: given parameters a,b > o and the given sequence x₁= b X = n+1 4 (x₂ + 4a) n Xn a. Show that a b.…

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

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Q: 00 1 n2 + 2n n=1

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Q: If Ea, converges and a, > 0 for all n, can anything be said about 2(1/a,)? Give reasons for your…

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Q: Which of the following inequalities can be used to show that +1 n=1 converges? 1 O n3 +1 nº + 1 O n°…

A: The series ∑n=1∞nn3+1. We have to find which of the following inequality can be used to show the…

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: Q4. If E a, converges and a, > 0 for all n, can anything be said about E2

A: Given that an is a positive term series and series an is convergent.   Here objective is to find…

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: en Σ n =1 n" converges Select one: True False

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Q: A sequence s, is said to be bounded above if there is some number N such that.... .a Sn =N .b .C…

A: Option d is correct.

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: Prove that if Ean converges , then (antanti+ --- anor)=0, Does it imply that Ean converges? Give…

A: Given: to prove, limn→∞an+an+1+.....an+r=0,r≥0

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: 00 For which a does > n(In n)a converge? n=2

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Q: so eskey ayン 1s Theorem : If En=1 an converges absolutely then it converges. 00 Н.W

A: Absolute converges means a series will converges even when you take the absolute value of each term.…

Q: If an < bn and if En=1 an converges, then 1 bn also converges. True False

A: we can solve it by using comparison test.

Q: If Ea, converges , then n=1a, diverges n=1 an n=1 Select one: O True O False

A: given sequence are, given that 1st sequence is converges and we have to find 2nd sequence is…

Q: b. Eel/n – el/n+1 n=1

A:

Q: Which of the following statements is true? O A. Η Σα, converges then Σ al converges. O B. В. Η Σα,…

A: To select: which statement about convergence is true.

Q: (-1)" is 3" (n + 1) n=1

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Q: Use only Definition 3.1.1 (or its negation) to prove the following: 2. Prove that the sequence…

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Q: The seies Σο, + converges to 1 16 n=1 Select one: O True O False

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Q: If an and bn both converge, then an bn converges. n=1 n=1 n=1 True False

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Q: Let n Prove converges. and Ž that the difference of these be goven fositive n%=D1 n= Seri es, Series

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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: 7L The sequence Converges to 2e Converges to 1 Diverges Converges to 0 O REDMI NOTE 9 PRO P AI QUAD…

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Q: What does Ek=1 converge to? Ak+11 k+12.

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Q: Test the llawing Seri es for being diverge Converge そ ) n +2 (-1) 30-1 (en)!

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Q: If > an converges, then a converges. n=1 n=1

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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: 1 The sequence converges to ,? – 1 – V n² +n | Select one: True 21 False

A:

Q: 5. The sequence r. is convergent in (R. d). a. True b. False

A: 5 - b , (false)

Q: Determine whether the sates is canergent or dNeroent, If it is convergent,find itS Scm 6+2+ 2. t. 4.…

A:

Q: Does a(n)= n^2sin(3/n^2) converge?  If so, to where

A: The given question can be solved as shown in step2.

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

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Q: Determine if the two given converges or diverges. { п n 2n + - 1/ n=1 Σ n n \2n + 1 n=1

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Q: 3. Σ n=1 n(n +3) 11 converges to Select one: O True False

A: Given series,             ∑n=1∞3nn+3

Q: (n!)³ (3n)! 321. n=1 8.

A: we have to solve using ratio test

Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence.  It was invented by German mathematician Carl Friedrich Gauss.