AAAAAA AAAA 30. If the power series an(x – 4)" converges at x = 7 and diverges at x = 9, which of the following n=0 must be true? I. The series converges at x = 1. II. The series converges at x 2. III. The series diverges at x = -1. (A) I only (B) II only (C) I and II only (D) II and III only Vietnam

Q: 6. Σ. 4n² - 9 n=1

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Q: 8. Find the sum of the series 5 if it exists. If no sum, write diverges on the blank provided. k=0…

A: Explanation of the answer is as follows

Q: 1. Determine if each series converges or diverges, you can use any of the tests discussed in class.…

A: a) ∑n=1∞3nen-1b) ∑n=1∞1+3n2nc) ∑n=3∞3n-14n

Q: The series elnz) - e) converge to n=1 (a)Ve - 1 (b) e - et (c)Ve - e3

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Q: 1. Consider the following two infinite series: 31 2k and 24 k (a) One of these series is NOT…

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Q: 2. Determine if the series converges absolutely, c a. E-1(-1)" (-1)7-1 c. E=1(-1)" n+2

A: These series are alternating series test  So for convergence first we apply this test  In which if…

Q: A. Write the first five (5) terms of the given series: an 2. a1 = 2, an+1 = 1. an = coS 3 1+ an

A: In this question we have to find first five terms of the given series.

Q: II. Determine whether the given series is convergent or divergent. Justify your answers. 22n 1. 3.…

A: (NOTE- According to our policy, only required to do the first three subparts) Ratio test- Let ∑anbe…

Q: 3 The sum of the series E, 'n = 1 1 is + 2" n2 +n Select one: 3 a. 2 b. 4 O C. 5 d. 3

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Q: es 1 + (-3) + (- 3)² + (- 3)³ + (- 3)* + ...

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Q: 00 Give an example of divergent seriesan and b, such that (a, + b,) = 1. n=1 n=1 n=1

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Q: 5"x3n Find the sum of the series: >(-1)" n! n=0

A: see below the answer and calculation

Q: 1. Determine if the series converges or diverges. State which test you are using. Show your work…

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Q: 3) For the geometric series 4 + 16x - 4 + 64x2 -16+ ... Find the range of values of x for which the…

A: We have to find the range of 'x' for whichGeometric series 4+(16x-4)+(64x2-16)+··········· converges

Q: 72 n²+1 7. Given a series En=1(-1)"-1 a. Determine whether the series absolutely converges or not.…

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Q: Expand the function , in a power series E a,x" with center e = 0. Find a,x". 7+8x n=0 (Express…

A: Interval of converges of the Power series

Q: 71.Š-1)"(nº + 1) en (-1)"(п3 + 1) 2. п4 + 1 (-1)"(п3 + 1) 3. 00 –1)" п3 +7

A: According to our guidelines, I solve first 3 subparts. Kindly request you to post the remaining…

Q: 2" 00 Find the sum of the series E n = 1 3" - 1

A: Given: ∑n=1∞2n3n-1 We know that the sum of infinite G.P is given by: S∞=a+ar+ar2+....+∞=a1-r Where…

Q: 1 by comparison to the geometric series. 1-x' Write the power series for

A: Power seriese expansion

Q: 6. What is the sum of the series 元 17 + πT TE (A) (B) (C) e+π e + 1 e اسه TU TT ++ (-1) +1/+ +... ?…

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Q: 2).  For an as follows, write the sum        an as a geometric series. a1 =  1 14 and  an an + 1

A: This is a question of infinite series.

Q: 1 5. Determine whether the series S= >) converges or diverges and identify the test you used. (3n +…

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Q: 4. For each series determine if it is convergent or divergent. Give reasons for your answers. (-3)*…

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Q: Consider the series (-1)+112n-1 n=1 (n+5)3 11+2 In this problem you must attempt to use the Ratio…

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