Given that 0 < an ≤ bn for all n, decide which statements, if any, are true according to the Direct Comparison Test. ∞ If bn converges, then an converges. n=1 If Σ anconverges, Σ bn converges. n=1 n=1 ∞ i̇ ∞ n=1 ∞ If Σ bn diverges, then an diverges. n=1 n=1 n=1 ∞ None of these. If an diverges, bn diverges. £₁ n=1

Q: If lim an 1 then n00 Σ an n=1 converges O diverges O may or may not converge

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Q: Suppose Σ XK is conditionally convergent, and define k=1 ak = max {xk, 0} and bk = min {xk, 0} ∞…

A: The objective of this question is to prove that the series Σa_k from k=1 to ∞ and Σb_k from k=1 to ∞…

Q: converges, because 0 < 1 and an %3D debook 2n + 1 2n +1 2n +1 Room

A: We have to choose the true or false

Q: ide which of the following statements are true and which are false. Prove the e ones and provide a…

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Q: Two of the following statements are true. Which ones? 8 If Σen (*1- x0)" converges, then en (x-xo)"…

A: Note that first and last option of your questions are same.

Q: Let {an}, and {bn}, are sequences of positive real numbers such that n=1 An lim 00. If A =E B= >) Σ…

A: Given that limn→∞anbn=∞choose an=n &amp; bn=1n2then limn→∞anbn=limn→∞n1n2=limn→∞…

Q: 11. g 13. F(r) = 3 r

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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 &gt; 0 for all n then ∑ 1an  converges         Proof :…

Q: Q5 MULTIPLE CHOICE One answer only We consider the sequence of functions (fn)neN defined on [0, 1]…

A: Basic application of limits will be used.

Q: Fill in the blanks in the following proof. Claim: Let xn = 1 + for all n E N. Then x,, does not…

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Q: Let amn 20 for all m, n. The following statements are equivalent : 1. E amn Converges by rectangles.…

A: We will solve this by the help of partial sum

Q: Let amn 20 for all m, n. The following statements are equivalent : 1. E amn Converges by rectangles.…

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Q: Let r E R satisty |r| < Let An = 5 Bn = 1 – r" , and Cn 2 - n 10 Note: The aim of this question is…

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Q: Write TRUE if the statement is always correct and FALSE if otherwise. Prove your answer. (a) If an…

A: The given statement is (a) If an≥0 for all n∈ℕ, then ∑n=1∞an does not converge conditionally.…

Q: In which of the following options, the statements given below and the general terms an that satisfy…

A: P-series test:  ∑an=∑1np  P-series is convergent for p&gt;1 and diverges for p≤1. 1) ∑an is…

Q: 1. Prove that converges. (hint: use the fact that 2n > n4 for all n> 100)

A: Since you have posted a multiple question according to guidelines I will solve first(Q1) question…

Q: 1. Σ 4n2 in 8n +3

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Q: 00 If 2a is converges , then lim a = ∞ %3D n=1 n- 00 صواب İhi

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

Q: M8 For which a does Σ n=2 1 n (In n)a converge?

A: To find the values of "a" for which the series∑n=2∞1n(ln n)a converges, use the integral test. Note:…

Q: Let an 20 for all n and suppose Σan converges. Prove that √an ΣΥ n converges. Hints: One way to do…

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