Let Ean and b, be series with non-negative terms. If a, 2 b, for all n >1 and Eb, converges, then a, converges

Q: Let an and > b, be two numerical series such that b, converges. Which of the following statements is…

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Q: Consider the real sequence {an} given by an = In(n+ 1) – In(n + 2), ne Z20 = NU {0}. Justify whether…

A: Given :  The sequence an given by ;              an = lnn+1 - lnn+2  ;    n≥1 To find :  To check…

Q: Let Ean and Eb, be series with non-negative terms. If a, > b, for all n > 1 and b, converges, then…

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: Suppose a, and bn are series with positive terms and b. is known to be divergent. (a) If a, > b, for…

A: a. Given that bn is divergent And an>bn for all n So an will always divergent. Note :- Super…

Q: In the given question as folows , verify that the infinite series diverges:- see the  equation as…

A: given: ∑n=1∞nn+1

Q: find

A: The series is given as, ∑n=0∞n!k+6k+6n!xn The value of an is, an=n!k+6k+6n!xn The value of an+1 is,…

Q: If the series En=1 an converges absolutely, the sequence {b,} is bounded, then the series sin(a,)b,…

A: ∑ann=1∞ is absolutely convergent and bn is bounded .

Q: If the power series E anz" converges at 2i, prove that the series also converges at 1 – i.

A: Given : The power series  ∑n=1∞anzn  converges at z = 2i. To prove : We have to prove that the…

Q: Determine whether the series is (are) converge(s) absolutely. 3* -1 A and D C and D None A and C

A: Solution is given as below:

Q: Suppose a and b, are series with positive terms and b, is known to be divergent. (a) If a, > b, for…

A: Given: ∑ an  and ∑ bn are series with positive terms and ∑ bn  is known to be divergent. a) If…

Q: If the lim,- (1+ = = e, then the series a, is Converge

A: (i) Since the limit is e that is not equal to 0. So by divergence test the given series diverges.…

Q: z=1 Vn+3 252. Σ (-1)*+1 Vn+3 1

A: By finding the sum we deduce the convergence of series as follows :

Q: Decide, whether the following series are convergent or not: c) (2k + 1)! k=1

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Q: ". ..., For each of the following, decide if the given series is a geometric series.

A: Geometric series is form in which power is increasing continuously              = A+ Ar+ Ar2 +…

Q: If the series un is convergent, n=1 then the series (−1)ª un is also convergent. n=1

A: Given first statement is true and second statement is false.

Q: Use the Comparison Test to determine if the series 2+ In n n sin? n n=1 converges or diverges.

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Q: Is the series 22"31-" convergent or dive n=1 Co

A: Introduction: We know that the series an=∑an converges only when L<1, diverges when L>1, Where…

Q: If 14 the Series Converges and is approximated with Ss, would the approximation be an overstatem ent…

A: We will first expand the series

Q: Assume E , is an infinite series with partial sums given by Sy 4 What is a,? A) B) C C) D) None of…

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Q: In the root test if p>1 than the series is diverges O True false

A: In this question, we need to find whether the given statement is true or false.

Q: Suppose that a is a number such that -9 an+1 -3)2n+1 n=0 convergent or divergent? If the series is…

A: given sequence is                                                      ∑n=0∞an+1(-3)2n+1

Q: Which of the series converge absolutely, which converge conditionally, and which diverge? Give…

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Q: Determine if the series 1/n14 , n = 1 to infinity converges or diverges. Explain.

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Q: Suppose a, and b are series with positive terms and b. is known to be convergent. in (a) If a, > b,…

A: Given query is to find select correct option regarding an and bn.

Q: If it is known that lim, ap =0, that is the k term of a series goes to zero as k goes to infinity.…

A: That's easy. Have a great day!!!

Q: Decide, whether the following series are convergent or not: eik a) (ik) k=0 k=0 k=1

A: Dear Bartleby student,according to our guidelines we can answer only three subparts, or first…

Q: The series from n=15 to infinity of n*(-6)^n/n! , does it converge absolutely, conditionally,…

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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: If the series(-1)"a, is convergent and the seies a, is convergent then we said the series (-1)"a, is…

A: To Check: Whether the series is absolutely convergent or conditionally convergent. Given: The series…

Q: 44. For which positive integers k is the following series convergent? laga Σ (n!)? sw Mong pe n=1…

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Q: Find the values of x for which the series converges. (If the answer is an interval, enter your…

A: Soling 1st question.

Q: Assume E, a is an infinite series with partial sums given by S, = 4+ What is as ? %3D h O k O

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Q: Suppose a, and b, are series with positive terms and b, is known to be divergent. (a) If a, > b, for…

A: We have two two infinite series with positive terms :∑n=1∞an and ∑n=1∞bn and also we have ∑n=1∞bn is…

Q: If the nth partial sum of a series a, is Sn = 2 - n6-", f is s, = 2 - n6-", find a, and E an n = 1 n…

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Q: Find the sum of the following infinite Series if it is Converges lo0 (l00) (100) (100)3 (100)" no,…

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Q: Use the Comparison Test to determine if the series 2+ In n Σ n sin? n n=1 converges or diverges.

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Q: If E an is a convergent series with positive terms, is it true that the series ( a) Σ(1+ α) (b)…

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Q: Use the Comparison Test to determine if the series 2+ In n n sin? n n=1

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Q: Decide if this series converges

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: n Sn = En-0 8 (-) 4.

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Q: Suppose Ea, and Eb, are series with positive terms and Eb, is known to be divergent. If a, > b, for…

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Q: If the nth partial sum of a series a, is s, = 2 – n6-", find a, and n = 1 ) an n = 1 a1 an (for n >…

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Q: Σ In n converges or dive ermine whether the series n=1 n conver

A: In this question, the concept of convergence is applied. Convergence The feature of approaching a…

Q: Use the Ratio Test to determine whether the series is convergent or divergent. If it is convergent,…

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Q: Suppose that ∑ an and ∑ bn are series with positive terms. Prove that if         and ∑bn converges,…

A: Consider the given limit, limn→∞anbn=0 by the definition of the limit we know that there exists an…

Q: Suppose >a, and ) b, are series with positive terms and) b, is known to be convergent. (a) If an >…

A: a) here last option is true,we can't say anything about series an.

Q: Consider the series , ark1, a 0. Then if r < 1, the series converges to

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Q: i) En=1 100 11

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Q: Determine whether or not these series converge, and if they do then to what.

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Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.