QUESTION 3 1 The series E is n=1 (3n - 2)(3n + 1) lim sn = convergent 3. OI. n+ 00 O I. lim sn = convergent 2 n+ 00 O I. lim sn = ∞ divergent

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Q: UESTION 13 The integral test can be used to determine whether or not E, =1 1 converges. O True o…

A: Since you have asked multiple question,as per our guidelines we are supposed to answer only one…

Q: n! x" For what value of x is the infinite series 2 diverges? O A. x = e O B. None of these. OC.x<e O…

A: Here the D-Alembert's ratio test is used for finding the value of x for which the given infinite…

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Q: If we differentiate the power series 12n+1 79 E(-1)n+1. %3D (2n + 1)! 3! 5! 7! 9! the resulting…

A: We will use Taylor's series expansion to find resulting power series.

Q: If an alternating series (-1)"a, satisfies lim, 00 an = 0, then it converges %3D Select one: O True…

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: 4. Recall the geometric series formula for all r <1, i.e. -1<r<1. Use this formula for the…

A: (a) Given ∑k=0∞rk=11-r ∴∑k=0∞-1kxk=∑k=0∞-xk=11--x        ∵∑k=0∞rk=11-r=11+x Hence proved.

Q: Find the series' interval of convergence and, within this interval, the surm of the series as a…

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Q: Example 1 Using the standard series, find the Maclaurin series for: (i) f(x)= sin(3x), %3D (ii) f(x)…

A: The function f(x) is a rule that associates or fixes a number to the particular point x. If y=f(x),…

Q: The following conditions imply that an alternating series E(-1)"an n=0 converges O (1) an is…

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Q: QUESTION 5 an+1 Assume thatlim an 1 does the series > 2"a, converge or diverges? n =1

A: For the series of the form, ∑n=1∞an according to the Ratio test,  check  for

Q: Test the series for convergence or divergence. n2 E(-1)" + 1, 3 + 11 n = 1 O converges diverges

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Q: ∞ (−1)n n ln(n) 6. The series (a) is Absolutely Convergent (b) is Conditionally Convergent, but not…

A: Solution:-

Q: Question 9 Consider the series E(-1)"x": 1. |r| <1 or the series Ea" 1. I피 <1. 1+x n=0 n=0 (9.1) Use…

A: We will find out the required solution.

Q: a n+1 =1 then the series is Suppose lim 71 Divergent Convergent Analytic inconclusive

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Q: e) Determine its limit an 1+8 an-1 %3D with do = 0

A: Since you have asked multiple questions but according to our company's guidelines I can only answer…

Q: QUESTION 13 a n +1 Suppose lim =1 then the series is а Convergent inconclusive Divergent Analytic

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Q: Which of the following geometric series are divergent? +00 +00 +00 ωΣ(5) «Σgn-1 α) Στ 3 n=0 n=0 n=1…

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Q: Question 2 Let E a, be a series of monotone decreasing positive numbers. Prove that a, converges iff…

A: Let ∑n=1∞an be a series of monotone decreasing positive numbers.we have to prove ∑n=1∞an converges…

Q: a) Σ 3"n 00 n!

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: 2. (Series) Determine if the following series converge or diverge. If it converges, find the sum. i.…

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