x" En=o n! Σ converges absolutely for all x

Q: {B"}-o; ß E (-1,0) A-Converges B-Diverges C-Absolutely converges D-Conditionally converges

A: According to our answering guidelines we can answer one question at a time, therefore I have…

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: 3 converges conditionally because lim n - 3 = 0. 3n + 1 3n + 1 True False

A: The given question is solved with explanation below.

Q: What are all of the values of x ,such that E-1)n+1(n)* converges? x1.2 O x<1.30 x<0,40

A: By lebnitz test we observe n^x tends to inf gives zero only when x&lt;0.

Q: 5. Find all values of x >0 so that ) converges. 3k k=2

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Q: a Let (n) be a constant sequence in R (i.e. there is some constant c such that In = c for all n).…

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Q: n n converges, because 0 < < 1 and an 2n + 1 2n + 1 ni an is decreasing. 2n + 1 True False

A:

Q: 5. Let ni < n2 < n3... be positive integers, and let E = x E [0, 27]; sup converges. Show that E has…

A: Given :  n1≤n2≤n3 ...  be the positive integers and E be the set defined as ;                E =…

Q: 1 Determine whether (-1)". converges conditionally, absolutely, or not at all. Vn2 + 1 n=0

A:

Q: Suppose ak > 0 and there exists M >0 so that E ak < M for all n E N. Prove that ak converges. k=n…

A: Suppose thatak&gt;0 and there exists M&gt;0 such that ∑k=0k=nak&lt;M , for all n∈ℕ. To prove that…

Q: Supposean converges conditionally (but not absolutely). Let A+ = {n €N : an ≥ 0} n=0 and A_ = {n € N…

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

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Q: 3.3 Prove that does not converge uniformly on R. k! k=0

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Q: en Σ n =1 n" converges Select one: True False

A:

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: V. Let f(x) be a differentiable function such that for all x > 1, f(x) • f(x) > 1, f'(x) (-1)" f(n)…

A: Solution is given below:

Q: What are all of the values of x ,such that converges? n=1 x>0.10 x1.30 x<1.40

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Q: Prove that E-1(a,/(1 + a„)) converges if a, > 0 for all n and Σε 1 ªn converges. 00 %3D

A: First, consider that series an converges. Given that all the terms are positive.   So,

Q: · E In (e + +) n = 1

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

A: We will use limit comparison test

Q: 3 - If E is convergent, find its sum. z=1 en n(n+3)

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Q: x" converges absolutely for all x Select one: True False

A: According to our company's guidelines I can only answer first question since you have asked multiple…

Q: If Ea, converges , then n=1a, diverges n=1 an n=1 Select one: O True O False

A: given sequence are, given that 1st sequence is converges and we have to find 2nd sequence is…

Q: 1. Let k € N. Determine all values of a such that Sink converges. an R

A: Suppose k∈ℕ and consider the series: ∑n=0∞nkanTo find: All values of a such that ∑n=0∞nkan…

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: cos(nT) n=D1 converges conditionally in Select one: O True O False

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Q: If E an converges, then an/n12 converges. n=1 n=1 O True False

A: True, using Abel's test.

Q: Prove that ∑^infinity_(n=1) ((-1)^n/n) converges.

A: Apply Ditichlet theorem.

Q: Prove that if 0 ≤ r ≤ 1 then (r^n) converges. Then prove that it converges to ???

A: We need to prove that |rn| converges for 0≤r&lt;1.

Q: (k!)* (2k)! k=1

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Q: n!n! is absolutely convergent using the Ratio Test. (2n)! 2. Prove n=1

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Q: +1 X What are all of the values of x ,such that (-1) n+ converges? 6 06.2 O 0<x<6.3O x26.4O

A:

Q: an = In(n+1) – In(n) for n EN determine if the following is convergent or divergent { an } n=1

A: Solving

Q: (a) f(0) = 0 (b) f'(0) = 0 (c) There exists another non zero sequence in (-R, R), yn, that converges…

A: This is a multipart question. We shall solve all the three parts for you. Solving this question…

Q: If fn If 0 ≤ an ≤ bn for all n € N, and f on [a, b], then lim ſå fn ‡ få f. an converges, then bn…

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Q: 1 1 = 0. Vn – 1+ /n converges because lim Vn – 1+ n n=1 True False

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: EXAMPLE f(z) = Σo(z"/n!) is convergent for all z and, according to Theorem 2.9, n7"-1 8 -n

A: Here we have to show step wise solve.

Q: Exercise 2. Determine whether the sequence of functions (fn)n converges uniformly on S. 1 fn(x) = S…

A: note : as per our guidelines we are supposed to answer only one question. Kindly repost other…

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: If > a, converges but |an] diverges then we can be sure that n=1 n=1 (a) an converges absolutely.…

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Q: n²sinx Show that g„(x) converges uniformly to x e [1,5]. 1+ n²x

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Q: the interval of convergence. (x+7)" ( a) Σ In n=1 x" (b) En! n"

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Q: SELECT ALL A. what condition/s would suffice to ensure A) B) Žaln) S& a(n) S&-Ea(n) converges…

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Q: an converges for some large k, then so will n=1 an- If E n=k

A: We have to check

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

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

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&gt;1.

Q: Vn2 +1 Prove that the sequence {an}n=1 converges by following the following sequence of steps n n=1…

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Q: nx +n² +x? Explore the uniform convergence of the functional sequence f.(x) = n² +x? on the set E =…

A: Differentiate the function fnx=nx+n2+x2n2+x2 with respect to x, and solve the equation fn'x=0. Apply…

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.