1 The scries n-7 Converges if n=1 A. p> 2 В. р> 2 C. p<2 D. p<2 E. p>1 F. p= 1 O F

Q: Prove that if {sn} converges to L and L &gt; 0, then there exists a number N such that sn &gt; 0 for…

A: Let sn be a convergent sequence and converges to L&gt;0. We have to prove that sn&gt;0.

Q: Jlgu (-1)" +1 Σ (3x)" What are all of the values of x ,such that 00 converges? n=1 x>02 C) x>3.3 O

A: Using ratio test the condition of convergence is:…

Q: Suppose a random experiment thar nas success probability p. Let X be the number of successes…

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Q: an Q4. If £ an converges and an > 0 for all n , can anything be said about E- ?

A: Given that ∑an converges and an&gt;0 for all n. The objective is to determine whether ∑1an converges…

Q: K+1 – /K k=1 VK² - +K

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Q: 3. Assume the sequence of positive numbers (sn) increases monotonically to infinity. Prove that Sn+1…

A: Let Sn be a sequence of positive numbers sn increase monotonically to infinity. ⇒limn→∞sn=∞     ∵ sn…

Q: 21. Show that E(-1)"+1; 2n converges n! absolutely. n=1

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Q: 1+ 1 + 1 V 3 + 1 43 Select one: Qa converges O b. It is inconclusive O c. diverges +...

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Q: Suppose that dz converges. What can we conclude about the constant p? Op>1 Op Op< 3

A: Explanation of the answer is as follows

Q: (-1)"+1 (3x)" What are all of the values of x ,such that converges? n=1 x>0.1 O 3.3 O .4 O 13 13

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Q: What are all of the values of x ,such that - (-1) n+A converges? n=1 .1 X26 .2 06

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Q: 3. Let for n € N. Is convergent? a₁ = 1, an+1 Σ n=1 = An sin an

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Q: 2. Suppose the sequence {sn} satisfies Sn+ 1 - Sn ≤ -1/24 n² For all ne N. Prove that {sn}…

A: Given that the sequence  satisfies .The objective is to find for all ,  converges.

Q: nk - k > 2 + 1' converges. n=1 Select one: O True O False

A: We will use limit comparison test

Q: 10. Give an example that Xn X but Xn does not converge to X in probability.

A: 10. Let Xn=-X, for n=1,2,3,... where X~N(0,1). Now, the CDF of Xn is FXn(xn)=PXn≤xn, for xn∈ℝ and…

Q: Let an > 0 and assume that an diverges. Write Sn = a1 +a2 + • ·.+ an. Prove the following…

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Q: The sequence {Pn =}1 converges n-1 to p = 0 of order a = %3D O a. 3 O b. 1 О с. 2

A: For some number p, if the condition limn→∞an+1anp=M&gt;0 is satisfied, then the order of convergence…

Q: Σ (-1)* converges. Vk Determine whether k=1

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Q: Let an > 0 and assume that an diverges. Write Sn = a1 + a2 + • ·.+ an. Prove the following…

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Q: 34. Assume that an+1/an converges to p = 4. -1 Does > an converge (assume that n=1 An # 0 for all…

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Q: 1.1 Determine whether the sequence {f.(x)} = {; on I = [0, 1]. converges uniformly %3D

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Q: Sn+(-1)") The sequence Converges to 1 Converges to 2e Diverges Converges to 0 Converges to e

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Q: that (An) rges in babilit to A II ntains a further subsequence that converges a.e. to X. only if…

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Q: A. Suppose Xn, n = 1, 2, 3, . . . is a sequence of random variables that converges in probability to…

A: Part A: Proof of Convergence in ProbabilityGiven:Xn​→PaYn​→PbWe want to…

Q: What are all of the values of x, such that converges?

A: We have to use GP sum Common Ratio.

Q: 1 7. Determine by the ratio test if n- converges or diverges. п! -

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Q: diverges. n=1

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Q: h reason or proof whether each of the fo ents of a sequence of random variables {-

A: *Answer:

Q: 2) Find the interval of convergence. (-1)"x" n? +1 Σ n=

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Q: s Find the sequence yt that satisfies the differenti al equation. mbrol of at: bes y₁. - 2y + ₁ +…

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Q: What are all of the values of x ,such that (-1)" -". 00 converges? n=1 x120 x0.4 0

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Q: k-1 2k-1

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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.