Which of the following statements is false? If E a, converges but E Ja, I does not converge, then a, converges conditionally. the above If E la, converges, then Ea,n converges. the above

Q: HW4 Prove the following E R° Jiverges if RE[I, o) and converges if RE[O,I) Hint: Prove |-R

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Q: 1 80. For which a does converge? na In n n=2

A: Consider the given series ∑n=2∞ 1na lnn There are three cases, Case-1, when a=1, then ∑n=2∞ 1n lnn…

Q: Show by example that E(a,/b,) may diverge even though Ea, and Eb, converge and no b, equals 0.

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

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

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

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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: Show that E-2 ((In n)ª/n²) converges for -o 1. n=2

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Q: Suppose that X₁, X2, ka)=P(X = _k) =1/2. Let Yn = Xn = n 2 Xi. are independent, such that, for each…

A: Chebyshev's Inequality Chebyshev's inequality guarantees that for a large class of probability…

Q: ht A: If S 2n – 2n²x x € [0, 1] fx,(æ) = { otherwise converges in distribution as n → 0. nt B: If 1…

A: Given that Xn : n≥1 is an infinite sequence of random variables and for each n, the density function…

Q: If an diverges and 0 (-1)"an converges. n=1 B)>(-1)"b, converges. n=1 c) 2(-1)"bn diverges. n=1 D b,…

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Q: 1 The scries n-7 Converges if n=1 A. p> 2 В. р> 2 C. p1 F. p= 1 O F

A: We have to find the value of p for which the given series converges.

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

A: I-M II-L III-K

Q: 29. Which of these statements is/are true? I. A sequence a, in R converges to a* if and only if…

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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: 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>1 and diverges for p≤1. 1) ∑an is…

Q: Let do = 1, a1 = -1, a; = (-1)" for 2" <j< 2"+1 and n e N. n2" Show that if |2 = 1 and z #1 then 1…

A: As per the question we have to show the inequality involving the partial sum. And then prove that…

Q: If E=1 an converges, then 5 (-3) an converges. n=5 O True O False

A: We are given two statements related to series and we have to state them as true or false.

Q: السؤال 9 What are all of the values of x ,such that ) (-1) n*1 converges? 6. n=1 06.2 O x26.3 0…

A: We will first find the radius of convergence, and then using it we will try to shape the interval of…

Q: Answer each of the following with convergent, divergent, or cannot conclude from given information.

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Q: If an > 0 and an converges, then (-1)"an converges. Select one: O True O False

A: Absolute Convergence test :The absolute convergence test states that, If ∑n=0∞anconverges then,…

Q: Explain why or why not Determine whether the following state- ments are true and give an explanation…

A: Hey, since there are multiple sub-parts posted, we will answer first three sub-parts. If you want…

Q: Q5. Which of the given converge! 3" 7" -2 n=1 b) n° +3n n°+ 7n +5 n=1 11 t 7 n=1

A: The given series are : a∑n=1∞3n7n-2b∑n=1∞n5+3nn8+7n+5c∑n=1∞n11+7nn7+n

Q: 25. Let a, := (), n2 1. Which of these conditions must be met if a, is to converge n+1 to 1? I for…

A: Note that for ε→0, 1ε-1→∞, thus from the condition n&gt;1ε-1, n→∞. Thus, the condition I is…

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

A: Given, the series ∑n=1∞nnp+1 Recall that p-test is :∑n=1∞1np is convergent iff p&gt;1 and divergent…

Q: 25. Let an := n 2 1. Which of these conditions must be met if a, is to converge n+1 to 1? I. for any…

A: Just use definition of convergence.

Q: a, > 0 and Ea, converges, then (-1)"an converges O False O True

A: This is Not True. Hence False is the correct answer. We will prove this by taking an example, Let…

Q: 7: Which of the following statements are always true? (i) E (-1y"e!/n converges. n=1 (ii) The…

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

A: Consider the given information: Here to match the statements and given general term an. Here option…

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

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Q: I En=1 an converges then 2a, converges.

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Q: (-1)h 7^ (n!)? 2? (an+3)! A)is diverget B)is absolutely convergent O is conditionally conveglat

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Q: Answer the following True or False: Suppose that a,20 for all n and that, (a,)" converges. Then a,…

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Q: Sn/2", l1/2". if n is a prime number otherwise. Let an Does Ea, converge? Give reasons for your…

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

A: P-test : Consider series ∑an=∑1np P-series converges only if p&gt;1 and diverges for p≤1. 1) Given…

Q: (a) If {an}=1 and {b„}n=1are both sequences of real numbers where 0 < an < bn and En=1 bn diverges,…

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Q: T or F , prove your answer Suppose (an) is Cauchy and that for every n ∈ N, the interval (−1/n,…

A: Statement is TRUE By the ARCHIMEDEAN PROPERTY AND DEFINITION OF LIMIT.

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

A: We consider each of the cases L,M,N and match them with I , II, and III

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

A: this is converges

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

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

Q: True or false? d) Suppose (an) is Cauchy and that for every n ∈ N, the interval (−1/n,1/n) contains…

A: If we select n to be a very large number then:  limn→∞1n=0 So the interval -1n, 1n is apporaching 0.…

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

A: Follow the steps.

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

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Q: Consider the following statements. (i) 2 (-1)"Cn must converge if cn > Cn+1 > 0. Сп n =0 1 (ii) 2 bn…

A: The 1st statement is saying that ∑n=0∞ -1n cn must converge if cn&gt;cn+1&gt;0 and the 2nd statement…