What are all of the values of x ,such that converges? n=1 1>0,1 0 <0,2 0 X>13 X<1 4

Q: What are all of the values of x such that (-1)"*" (3x)" converges? 10 x>0.20 3. r>3.40 1/3

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Q: 5) The interval of convergence is: a) (-2,2] b) (-2,2) ed to show that c) (-2,2) d) [-2,2] ()…

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Q: Determine whether the given converges or diverges. n Σ 2n + 1 n=1

A: Given is a series ∑n=1∞n2n+1n To check if the given series is convergent or divergent Ratio test:…

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: 2* converge? If so, what does it converge to? If not, justify. 7k 1 2 2. Does

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Q: Find all numbers x such that the series n=1 converges!

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

A: To solve this question we shall use root test for series.

Q: Use the Ratio Test to prove that  ∑ (2/3) (n-1) converges. n goes thru n=3 to ∞. Write step by…

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Q: Find all values of x such that converges. n! n=1

A: Given that, series ∑n =1∞  xn2n! Compare the series ∑n =1∞  xn2n! with its standard form ∑n =1∞  an…

Q: Find all values of x such that ΣΗ converges. n! n=1

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Q: What are all of the values of x ,such that (-1)"*'(n)* converges? n+1 U). n31 x14O

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Q: a n+1) %3D 2n Ans. Converges, 6)

A: Since you have posted a multiple  question according to guildlines I will solve first (Q6) question…

Q: (-1)" converges conditionally. Inn Show that n=2

A: For the solution follow the next step.

Q: · E In (e + +) n = 1

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Q: ? 4. Show that the sequence {fn}, where nx fn(x) = XER 1+n²x²⁹ is point-wise convergent but is not…

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Q: (n + 1)? n3 + (1.1)" 350. n=1

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Q: Determine whether the given converges or diverges. n 2n +1 n=1

A: We can solve this as follows:

Q: 6" Using the ratio test, determine if converges or diverges (n + 1)"

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Q: What are all of the values of x ,such that Σ.. (-1)" + 1 converges? (31)"

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Q: * :use convergence test on the function an = (1-1)" with nth root test n B) diverges C) equals 1 A)…

A: Solution:

Q: 2 n 1 o Show that + converges/diverges n-

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Q: Let {xn} be a sequence of real numbers. Let yn be the average of the first n-terms: x1+ x2 + Yn + Xn…

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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: The series O True O False Σ (-1)^+1 n=2 n3+1 is absolutely convergent.

A: The given series is summation of (-1)n+1/(n3+1), n from 2 to infinity.

Q: 22n Σ n! n=1

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Q: The series True O False Σ n=1 (-1)"-3 √n is absolutely convergent.

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Q: (-1)" In(n) Vn n=2

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Q: Let {xn} be a sequence of real numbers. Let yn be the average of the first n-terms: x1+ x2 + Yn + xn…

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Q: αn = 2^n + 3 · 5^n / 4^n + 5^n  where  n = 1, 2, . . . . Show that {αn} con

A: Convergence of a sequence: Let an is a sequence and limit n→∞ of the function an is limn→∞an=p. Then…

Q: 3n 4. Use the ratio test to determine whether Σ converges. (n + 1)! n=1

A: use the ratio test for convergence of series.

Q: 1 1+ 2/2' 3/38 1 1 + 1 + ... 5/5 +

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Q: F) nー1

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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: What is the convergency interval of (2n)l

A: The given series is,  ∑n=1∞n!23n2n!xn To find its interval of convergence.

Q: fn(x) = { n2x for  0<=x<= 1/n, -n2x + 2n for 1/n<= x<= 2/n, 0 for 2/n<= x<= 1., is uniformly…

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Q: M Z(1-nsin-) converges n = 1 Select one: O True False

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Q: an conditionally converges then Jan] converges. n=1 n=1 True OFalse Rationale: Reset Selection

A: As per our guidelines we are allowed to solve one question at a time. Kindly repost the rest…

Q: 6. SELECT ALL APPLICABLE C A) converges by root test 1 10n+1+(-1y" B) converges by ratio test B D. E…

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Q: Suppose that p(x)=an" converges on (-1, 1], find the interval of convergen n=0 8 left end included…

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Q: 26. The interval of convergence for (X-3)* k - (x– is а. (-3, 3] b. [-3, 3] с. (-2, 4) d. [2, 4] е.…

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Q: n+ 7) ) Σ n2 n=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: 7n+2 5. By using Ratio Test, determine whether > converges or diverges. (n + 1)! n=1

A: The answer is found in step-2

Q: Use comparison test to show that the series E=1 (2) converges. 5n2-п.

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Q: Show that n* 3-" converges for all exponents k. n=1

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Q: O Does Eo 2k+² e-k converge or diverge? If it converges find the sum. "k=1'

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Q: The series 2 1 is convergent. n =1 n(2) Select one: O True O False

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Q: 5. Use one of your comparison tests to decide if Σ n+1 converges. Justify your n° – 2n² – 7 n=3…

A: The given series is ∑n=3∞n+1n6-2n2-7

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.