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

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: an a) Converges n2 b) lim an =0 > cans converges dd) > cos (an) Converges n=1 e) Cos can) diverges

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Q: Σ 2n n? + 2n h= 1

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Q: An. If > an converges for some large k, then so will n=1 n=k Select one: True False

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Q: n² – sin(n) nº + n² 1. Determine whether is absolutely convergent, conditionally convergent, or…

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Q: 1 1 Зп — 1 3n + 2 n=1

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Q: Let a, = 2n+1– 2". Then, lim an %3D n-00 None of the other options the above co and the sequence…

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Q: n=1 (ii) Give an example such that a, converges conditionally and diverges. IM:

A: Please see the below picture for detailed solution.

Q: nl n-1 lim O converges O diverges

A: Given query is to find series converges or diverges.

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

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

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Q: If lim an 0 then an diverges n- 00 n=1 O True False

A: There is a theorem which states that: statement: if a series ∑n=1∞an of real numbers converges then…

Q: tate whether the sequence an = e¯nl7 converges and, if it does, find the limit. -1/7 ) O converges…

A: finding limit

Q: 2n Let an = 3n +5 Determine whether {an} is convergent. Determine whether an is convergent.

A: To determine whether the given sequence and series is convergent or not.

Q: tion 35 Suppose lim an = 00 and an1> a, > 0 for all n> 1. Which of the following statements must be…

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Q: Petermine whether (-1)k converges absolutely, converges conditionally, kl/2 k=1 diverges. or

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Q: Let a, = vn +1– yn. Then, lim a, = None of the other options -00 and the sequence (a,,} is divergent…

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Q: Q1:- (A) Discuss the convergence of the given sequence : a(n) = cosh ln(n) (B) Evaluate: f dxdy…

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Q: ne wheti wheth the ser 00 (-14)" n! n=0 psolutely convergent onditionally converge

A: Here we have;  ∑n=0∞(-14)nn! ∑n=0∞(-14)nn!=∑n=0∞an   (let)⇒ an=(-14)nn!

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

A: We will use limit comparison test

Q: Let an = 2"+1– 2". Then, lim an = %3D n-00 None of the other options O the above co and the sequence…

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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: 8. n2 - 1 A)E n³ + 4. n=1

A: ∑i=1∞ai is said to be CONVERGENT if the sequence of partial sum results in a finite limit value for…

Q: Apply the Ratio Test to determine convergence or divergence, or state that the Ratio Test is…

A: Given that: ∑n=1∞enn!

Q: etermine and justify if ∞ In(x) k=2 (1+k) ³/2 converges or diverges.

A: given series ∑k=2∞ln(x)(1+k)3/2

Q: N 2N + 1 2) Show that converges/diverges. +

A: We have to show whether the series converges or diverges.

Q: 6 Let an 3n + 1 (a) Determine whether {a,} is convergent. convergent O divergent (b) Determine…

A: We can find the answer as below.

Q: (0) If lan diverges and (an Converges, n=1 (a) An Converges absolutely. n=D1 (b) Y An Converges…

A: We will get the conclusion by using the definition of a conditionally Convergent Series.  Option (b)…

Q: +00 El-1)» (" – n)" 2η n=1

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Q: n = 1 Vn lim n-00 converges O diverges

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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: 5. If En-1 an converges, and if an +1 and a, > 0 for all n, (a) Show that E a converges. (b) Does E1…

A: Since, the sequence is a positive monotonically decreasing sequence, so, is also monotonically…

Q: 8. n2- 1 n = 2 convergent divergent If it is convergent, find its sum. (If the c

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Q: (iii) 2 an must converge if lim an 0. n =0 bn (iv) 2 bn must diverge if b, > 0 and lim = 4. n->0…

A: The solution are next step is

Q: 1 diverges if it is true. An 6. Suppose An converges. Assume the terms an are non-zero. Prove n=1…

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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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Q: If lim,→00 an 0 then an converges. Select one: O True False

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Q: an If a, + 0 for all n > 1 and lim |-" | , n→00 an+1 an n=1 converges. True False

A: We have to tell that given conditions are true or false.

Q: 2n Let an = 3n +1° (a) Determine whether {a„} is convergent. (b) Determine whether a, is convergent.

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Q: Inx? x² –1, 2 x=2 A-Converges B-Diverges C- Absolutely converges D-Conditionally converges 8.

A: In both cases we use comparison test.

Q: Determine whether the scries is absolutely convergent, conditionally convergent, or divergent. (a) E…

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Q: 5n Let an 6n + 1 (a) Determine whether {a,} is convergent. convergent divergent 00 (b) Determine…

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Q: If a <b <c If lim a =L and lim c =L+7, then which of these is TRUE? n- 00 n- 00 OA (b can either…

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Q: 6. If > an converges but >lan] diverges then we can be sure that n=1 n=1 (a) an converges…

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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: If 2(-1)" a, is absolutely convergente the n=0 na, is divergente. Select one: O True O False

A: Topic:- sequence and series

Q: diverges if it is true. an n=1 Suppose > an converges. Assume the terms an are non-zero. Prove > n=1…

A: Consider the given information: Let ∑n=1∞an is convergent series. The terms of an are non-zero. To…

Q: 6) If an converges, then n=1 a) E converges. n=1 b) lim an = 0. n00 00 c) E(an)² converges. n=1 d) E…

A: Disclaimer: Since you have asked multiple questions, we will solve the first question for you. If…

Q: Let a1 = 1 and an+1 = [1-1/(n+1)^2]an for all n ≥ 1. 1) Show that the sequence {an}n≥1 converges.…

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Family of Curves

A family of curves is a group of curves that are each described by a parametrization in which one or more variables are parameters. In general, the parameters have more complexity on the assembly of the curve than an ordinary linear transformation. These families appear commonly in the solution of differential equations. When a constant of integration is added, it is normally modified algebraically until it no longer replicates a plain linear transformation. The order of a differential equation depends on how many uncertain variables appear in the corresponding curve. The order of the differential equation acquired is two if two unknown variables exist in an equation belonging to this family.

XZ Plane

In order to understand XZ plane, it's helpful to understand two-dimensional and three-dimensional spaces. To plot a point on a plane, two numbers are needed, and these two numbers in the plane can be represented as an ordered pair (a,b) where a and b are real numbers and a is the horizontal coordinate and b is the vertical coordinate. This type of plane is called two-dimensional and it contains two perpendicular axes, the horizontal axis, and the vertical axis.  

Euclidean Geometry

Geometry is the branch of mathematics that deals with flat surfaces like lines, angles, points, two-dimensional figures, etc. In Euclidean geometry, one studies the geometrical shapes that rely on different theorems and axioms. This (pure mathematics) geometry was introduced by the Greek mathematician Euclid, and that is why it is called Euclidean geometry. Euclid explained this in his book named 'elements'. Euclid's method in Euclidean geometry involves handling a small group of innately captivate axioms and incorporating many of these other propositions. The elements written by Euclid are the fundamentals for the study of geometry from a modern mathematical perspective. Elements comprise Euclidean theories, postulates, axioms, construction, and mathematical proofs of propositions.

Lines and Angles

In a two-dimensional plane, a line is simply a figure that joins two points. Usually, lines are used for presenting objects that are straight in shape and have minimal depth or width.