If da = 00. Then 1211 Select one: a. converges but we don't know the sum of it. b. diverges. C. We can't decide. d. converges to oo.

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: By 6/2silon definition, check the Convergenre of the following Sequenies. = 2n21

A: Given that, Sn=2n2+12n2-1 We find the limit of this sequence as follows:…

Q: Q1: Investigate if the following sequence converge or diverge 00 3n2-1 In D0 10n+5n?

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Q: Evaluate the following and determine if the sequence {a,} converges or diverges 20n2 5n +1 - an %3D…

A: Given,

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Q: Write the first five terms of the sequence, give the exact answer: +oo In+11) n=1 Determine whether…

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Q: Find the sum, if it converges. 7i-1 ΣΤ 10 The sum is (Type an integer or a simplified fraction.)

A: Given,             ∑i=1∞ 7710i-1

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A: The given terms converge for large values of n if r≤1 a) Given r = 0.75 <1 Hence convergent.   b)…

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Q: find if it converges ∑∞ n=0((4n)!(1103+26390n))/(3964n (n!))  (show each step please)

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Q: Which one of the following sequences does converge to 0? (-4)" an a. n! Зп +1 -)" Зп - 1 O b. an =…

A: To find which of the following sequence converge to 0. By using ratio test first and fourth option…

Q: Which one of the following sequences converges? OA. OB (-1)" 7 5" oc (-1)" n 7n +2 n? OD (-1)". 5n +…

A: Disclaimer: "Since you have asked multiple questions, we will solve the first four question for you.…

Q: Which one of the following sequences converges? OA (-1)". бл + 3 OB. (-1)"- 4n + 6 4n OC In(6n) OD…

A: if limit of an is finite then sequence is convergent

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Q: Use all three methods, (difference, quotient, and derivative) to determine if the following sequence…

A: We can use addition or subtraction method To check whether  following sequence is increasing or…

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

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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: Which of the following is true for the sequence, Vn? sin(n2) n3 +1 an = Converges to 0. o Converges…

A: Given sequence is  n32sin(n2)n3+1

Q: State whether the sequence an = sin converges and, if it does, find the limit. a) Oconverges to 1 b)…

A: If f is continuous and {xn} converges to x. Then f{xn} converges to f(x).

Q: n+1 –1)' b) An Vn

A: Consider the sequence is, an=-1n+1n3 Then, an=limn→∞1n13=1∞13=0 As n tends to infinity the sequence…

Q: Q1/ Is the sequence {a,} converge ? an

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Q: Write out the first five terms of the sequence {n sin÷.. and decide if it converges. n=1

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Q: Determine whether the seauence converges ordiverges. If it conveges, find the 00°+n100+(Inn)loD an=

A: Let an=100n+n100+(ln n)100+100n+n+1

Q: 1 Q:: If En=1 find the following: - Vn+1+vn 1- The sum of sequence? 2- Determine, if the sequence…

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Q: 3 n° Cos n+ 5n J

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Q: The radius of convergenE of 710 5.30 None.4 0

A: Option (2) is correct.

Q: The sequence n0.1 converges if

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Q: RIO

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Q: If the sequence {|]} converges to L, then the sequence {-m}converges to -L. Select one: O a. False O…

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Q: Choose the letter of the correct answer. Which of the following is true? The sequence whose nth term…

A: Solution of given question is written in below steps.

Q: Vn+I-yn 205. n

A: we have to test whether the given series is convergent or divergent

Q: Give the sequence an = 3n/5n From what I can tell the sequence converges but what is the value?

A: Sum =a/(1-r)  a is the first term r is the common ratio.

Q: + inf 1 Σ п2 — Зп + 2 n=3 W

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Q: Which one of the following sequences does converge to 0? O a. 9, = (+1yn an= Зп - (-4)" O b. an n!…

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Q: ii. ) -3(n+1) -3n e n=1 If it converges, state the number that it converges to. If it diverges to,…

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Q: B: To what value the following sequences can converge: Vn+3 %3D 1 4n+3 -Inn 2n2+1 1) an= 2) a,…

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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: The sequence a,=n sin 1 converges Select one: True OFalse

A: We have to check

Q: The general term of sequence I,Ź stanting by n =D0 is

A: By taking limit from n=0 to 3

Q: Given: a, = In(n + 1) – In(n) for n E N Σ An n=1 2.

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Q: Consider the sequence {x} defined by n n+1 +In(1/n²) ifnis odd Is the sequence divergent or…

A: Since answering more than one question is not in our scope, rest can be reposted.

Q: Find the sum, if it converges. Σ6 i= 1 The sum is (Type an integer or a simplified fraction.)

A: In this question we have to find the sum if the series is converges.

Q: Using the same proof that we saw in class that shows that n-1 7 converges, prove that n=1 na…

A: Given the series ∑n=1∞1n2 converges. To show that the series ∑n=1∞1nα converges when α>1.

Q: Q1/ Isthe sequcnce {a,} converge ? -(1 -4)"

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Q: What about the sequence an =16 + (10n2+1)/en for all n.  Is it monotone? Does it converge?  If so,…

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Q: Suppose a,>0 for all n and 2a, converges , which of the following must converge: n=1 Select one: a.…

A: We have to check

Q: Write the first five terms of the sequence: ( +o0 S11 In n n=1 Determine whether the sequence…

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Q: 1+ k 34. -

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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.