Prove for uniform covergence the series 1 „VxeR. (By using Weierstass's M-test). 5 7 2 n=1 n" +n'x?

Q: 2. Test the Convergence of n ! nっl nn Fnd frarier series of Hhe functin -T/2 <X <T/2 of the function…

A: Ratio test :If ∑an be the positive term series and L=limn→∞an+1an  , then(i) If L&lt;1 , series will…

Q: +0 Σ (2х — 1)" n V4n + 1 n=0

A: The given power series is ∑n=0∞2x-1n4n+1. Find the interval of convergence.

Q: 2. Find the interval of convergence of the series (n + 2)(x + 3)²n+2 2n

A: Here an=n+2x+32n+22n. The series converges if limn→∞an+1an&lt;1

Q: Since lim k→+0 (k + 1)!/3k+1 k!/3* k+1 lim k→+∞ 3 +00, k! the series…

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Q: the Following Series for bein divergent Test Con vergent or Cn +us! tan n 2. 1+ n W aW

A: Since you have asked multiple questions in a single request, we will be answering only the 1st…

Q: VI. Give the Maclaurin series expansion of f(x) = In(2 - 3x). Determine its interval of convergence.…

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Q: Find the interval of convergence of the series. (x - 4)n Σ 8+ 5n n=0 45 19 <x< 8 -1 < x< 9 -1 sxs9…

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Q: Use the Integral Test to determine the convergence or divergence of the p-series.

A: Integral Test: If ∫1∞fx dx  converges,  then ∑n=1∞ an converges If  ∫1∞fx dx  diverges,  then ∑n=1∞…

Q: 2 – n I-2 n3 +1 n=1 3

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Q: (7) Express the function h(x) = -1 tan(2x) as a power series. Show your work. Hint: tan(2x) = |…

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Q: the Po lowing for being Test series Convergenl- divergent or (4n-5)" (오nti)^ Cos W W:

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Q: Help please

A: To determine whether the given series is converges or diverges.Consider the function

Q: f(x)= 1/(1+x)2

A: Given:fx=11+x2 Formula used:…

Q: (−1)n! What is the Find the Taylor series for f centered at 4 if f¹" (4): 3″(n+1)* radius of…

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Q: 43. (n!)2 Σ (2n)! n=0

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Q: 3. For the series n=1 a) Use the Integral Test to show that the series converges. Suppose that the…

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Q: s) Show that the Maclaurin series for e" converges to f(x) 3 e", for || < ∞ %3D

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Q: The radius of convergence of about Xo=o (1-メ)

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Q: Find the Taylor series for f centered at 6 if (-1)^n! 3"(n + 1) fln)(6) = Σ( n = 0 What is the…

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Q: 08 n=1 n/n In(n²) 100 3. Ση-2.

A: We need to find series converges or diverges by using. integral test

Q: i) Prove that the series sin nx n2 n=1 converges pointwise on R, and uniformly on any finite…

A: Since you have posted a question with multiple sub-parts, we will solve first three sub- parts for…

Q: b)I,- ;: Use the Comparison Test to test the series .7 Σ 2 + n° n=1 for convergence or divergence.

A: Given: ∑n=1∞n72+n9Query is to use Comparison test and find that the given series is convergent or…

Q: (1)" n2 (5x+20)" 4nti

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Q: Evaluate using McLaurin's Series of Expansion and integrate from the indicated limits from 2 to 4.…

A: The solution are next step

Q: Find the radius of convergence of the power series >2 an z" where m=2 S 2", if n is prime 0,…

A: Given power series, ∑n=2∞anzn here an=2n, if n is prime0,  otherwise Find the radius of convergence…

Q: The radius of convergence of a series is (6n+1 (z – 2i)" 2n+5

A: recall:Radius of convergence of power seriesA series of the form ∑n=0∞ anz-z0n,where an∈c and z0∈c…

Q: Find the radius of convergence for the series 3 n³ xn 3n OR=3 O O OR= 8 n=1 R = R= - الله R = 1 8

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Q: Let's determine the correct radii of convergence for these series. (2x + 7)" Σ 5h Seç. T-1…

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Q: Use Founler series methad to the inhungerens heat equathon t>o, nE CO, boundary data: ult, o) z u…

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Q: 2. Using the fact that D₁ ((2 − x)−¹) = (2 − x)-², find the Maclaurin series for 4x³ f(x) = (2 -…

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Q: 3. By integral test, Determine the convergence and divergence of the following series. 1 Σ Vn+4 n =…

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Q: Show that the following series is divergent using the Test for Divergence. 4k³ - 1 k³ + 5k² + k k=1

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Q: a. Find the Interval of Convergence and Radius of Convergence of f defined by the power series. тn!…

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Q: 1 Given that Σ 1 x" with convergence in (-1, 1), find the power series for with center 1- x 1- 3x9…

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Q: Determine the radius of convergence and interval of convergence for the pow п+1 (x-2)" n=0 (2n +1)!…

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Q: Does the series from n=1 to infiniity of 1/(n^2+9) converge or diverge using the integral test?

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Q: Expand the function using Maclurin series expansion. f (x) 2 arctan y

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Q: liin x* ) メーマの (scin (seinx) - xa-x?

A: We are given :limx→0x-5sin(sin x-x1-x23)=limx→0sin(sin x)-x1-x23x5=limx→0(sin(sin x)-x1-x23x5x5x5=∞

Q: The series from n=0 to infinity of [8^n/(9^n+6)] is given.  Using the direct comparison test,…

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Q: Determine convergence or divergence of the series by Integral Test 1 E (2k + 1)(3k + 1) k=1

A: Solving using integral test

Q: Determine the interval and radius of convergence for the power series. 2k kz (x + 2)k k=1

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Q: Find the radius of convergence of the series 2" O 1/2 O1 O infinity IM:

A: Answer : radius of convergence of the series is 2

Q: Show that the series f(x) =) Sinx/n Converges uniformly IR n=1 want to show f(x) = sin x/n converges…

A: We will use the basic knowledge of the theory of sequence and series of real-valued functions to…

Q: 26. Show that the series is divergent using the Integral test 1 n=2

A: ANSWER :

Q: 2. Find the region of convergence of the series (3r)" n +2

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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.