3n2 ? Which of the following is TRUE about the series. Consider the series 2(-1)"b,, where , (20% + 1) 2-1 lim an=0 and the series is covergent OA. OR lim bn = 31400 and series is divergent lim and the series is convergent OC. lim an=31400 and the series is convergent OD. lim =-3/400 and the series is divergent OE.

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Q: 4.For what values of x , does the series, 1--s)+r-s} -r-s) +. (x – 5) + 27 (x - 5)" + converge ? If…

A: Simplification and integration

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A: Given that ak=k!2(2k)!2or, L=limk→∞(k+1)!2(2(k+1))!2k!2(2k)!2or,…

Q: +00 1 Σ 4n² – 8n + 3 n=1

A: Convergence of series

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Q: Let the series 2. 3" be given. Which of the following is false for the divergence of this series? 2"…

A: Option B is correct

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A: Expand series

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A: Solve by series interval of convergence

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Q: P 1. Use the integral test to determine whether the series En-2 n(In(n))3/4 convergent or divergent.…

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A: Apply series ratio test and find whether the series is converges or not.

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A: We have to solve the given problems.

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A: In the given question we have to find the sum of the series and the region of the convergency of the…

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Q: se any method to determine whether the series converges or diverges. (k !)6 Σ (6k)! k=0 O The series…

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

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A: In this series we have to find whether the series is convergent of divergent.

Q: Consider the following series. 1+4" 6" (a) Determine whether the series is convergent or divergent.…

A: (1) Ratio test: The ratio test is used to test the convergence and divergence of the power series.it…

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A: To apply root test, we transform given series to new series where x is taken arbitrary.

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Q: 1 Find the value of the integral 1₂ Determine whether the series ∞ dx 2 9x (ln(3x))² n=2 1 9n…

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Q: Show whether the following series are convergent or divergent. If the series is convergent determine…

A: To find the given series are convergent or divergent and if convergent to determine the value of it.

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Q: 10. For Z 1/n, a) write the first four terms of the series; b) use the integral test or the p-series…

A: Answer and explanation is given below

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Q: The value of x for which the series - OA25x<3 or 3<x≤ 4. OBx<2 or 4<x. OC. None of the choices in…

A: We will solve this question by first calculating the radius of convergence of the series.

Q: Consider the following series. 1+3" 4" (a) Determine whether the series is convergent or divergent.…

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Q: +oo Consider the power series 22n (2x – 1)". n=1 Determine the radius and interval of convergence of…

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Q: Consider the series 2n Σ n=0 3n +1 by the test of divergence, O lim a, #0 , so the series diverges n…

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Q: 2. If the power series > an(x – 4)" converges at x = 7 and diverges at x = 9, which of the following…

A: Power series converges at x=7                            diverges at x=9

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Q: Consider the following series. 1+8" (a) Determine whether the series is convergent or divergent. o…

A: In this question we have to find the series is convergent or divergent.

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A: 1. Given series is ∑n=1∞5nxn(n+1)n+11 By Ratio test we get limn→∞5n+1xn+1(n+2)n+12×n+115nxn(n+1)…

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Q: (-1)"x2 Is The interval of convergence of the power series 22n! Select one: O a. (-00, 00)

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Q: Consider the series: In (1 + ) In(n)ln(n + 1) Express this series as a telescoping series: (1+)…

A: The given expression is:…

Q: Given the power series Σ (x+ 2)" n =0 2" Find the "Interval of Convergence" for the series.

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Q: Find the interval of convergence for the given power series. * n1° (x + 6)" (9")(n ) 32 n=1 The…

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Q: 2.1 Consider the power series a,(2 – 2+ 3i)a". (a) If 0 < L < ∞ i the radius of convergence of the…

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Q: 7) FIND THE MACLAURIN SERIES FOR 8) FIND THE INTERVAL OF CONERGENCE fex) = x Cos (2x) FOR ? (-1)"x^…

A: Given  fx=xcos2x To do Find the Maclaurin series for fx

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A: Given that ∑n=0∞an(4x-8)n converges when x=-3. So, 4(-3)-8=-12-8=-20. (1) The aim is to find the…

Q: Q2.Use n-th term test to test the series: E (-1)" Vn+ Jn – In. n=1

A: To use the n-th term test to test the given series.

Q: 1 Question 4 Determine whether the series )` converges or diverges. Be sure to name any test(s) n ·…

A: