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

Q: Ex. Show the seguence whose nth term is In (n*) an %3D converges. 5n

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Q: Find the interval of convergence of ∞∑n=0 (x−2)^n/n+ 3

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

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Q: 3) For which a does > Σ 1 converge? Justify your answer. n(In n)a n=2

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Q: For which values of x does > n!x" converge? n=0

A: To Determine: for which value of x does converges? Given: we have a power series  ∑n=0∞n!xn…

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: How would I find if the sequences an=nπ cos(nπ) and an= (n2)(1/n) are convergent/divergent?

A: To examine the given sequence regarding convergence, that is study the limits as n tends to infinity

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

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Q: Given that lim n2(x- 5)" converges by the Ratio test. If x€ Z then the numerical n- 00 value of x is…

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

A: The ratio test states that: if L &lt; 1 then the series converges absolutely; if L &gt; 1 then the…

Q: (b) Use the comparison test to determine if the following improper converges: 5/T +1 7+x + x²

A: According to the given information it is required to check for the convergence: ∫1∞5x+17+x+x2dx

Q: Show that > iP converges to a finite value iff p < –1. i=1

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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: Suppose that an(x – 6)" converges for x = 10. At which of the points (a)-(d) must it also converge?…

A: Given: The given series is ∑an(x-6)n  The series converges at x=10. According to theorem is the…

Q: Find all values of x for which ) (3x)" converges. n=D1

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Q: (3n)" (2n + 50)" n=1

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

A: Using ratio test a series converges iff:…

Q: Š V2n-5 n=1 n2- 3n +4

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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: 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^n+2 / 5^n converge or diverge?

A: f(n)=3n+25n=3n325n=9(35)n The sequence converges as 35&lt;1.

Q: Suppose that anx" converges for x = 5. Must it also converge for x = 4? What about x = -3?

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Q: . Find all values of x for which пх" n=1 (n + 1)(2x + 1)" converges absolutely.

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Q: Σ Show that n2 + 1 converges/diverges n

A: The given series is: ∑n=1∞nn2+1 Let  an=nn2+1,n≥1    =nn21+1n2   =1n1+1n2 And, bn=1n

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

A: We can solve this as follows:

Q: Are there any values of x for which E=1(1/nx) converges? Give reasons for your answer.

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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: The interval of convergence of +∞ x2n Σ(-1)" is (2n)! n=0

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Q: E (1- nsin-) converges n = 1

A: Series convergence test problem.....

Q: 1 3) For which a does converge? Justify your answer. n(In n)e n=2

A: This question is related to series.

Q: 103n2 – 8 - 1. Xn := 4n2 + 99n + 3 1i. Xn := -n + Vn² + 3n 3n? + 2n iii. Xn := 2n n=1 8.

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

A: We have to use GP sum Common Ratio.

Q: Find the convergence set (or interval of convergence) for the 80 (x-2) Σ 6n+8 n=0 1.

A: Solution

Q: The sequence {x}=0, where xn (A) True (B) False 20 = is convergent. n!

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Q: (1) Show that n2 +1 n=1 converges conditionally. Show that all conditions of the test used are…

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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: What test would you use to test the convergenc 2n+1 n=1 n³-4n²+6 2. ΣΤ-1 (-1)"+1 (n²+3)² 3. Σ-1 5sec…

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Q: Show that 2"x" converges if |x| <. n=1

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Q: Find the values of p such that E(-1)"- converges.

A: The given series :

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

A: We have to check

Q: Find the interval of convergence for  ∑∞ n=2 (x^n)/((n^2)(3^n))

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Q: Determine if the two given converges or diverges. { п n 2n + - 1/ n=1 Σ n n \2n + 1 n=1

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Q: 3k 5- 2k+1 k=1 2 1. Does converge? If so, what does it converge to? If not, justify.

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Q: 30レて

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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.