32 E. For the given series, S2 = 10 and S = what is the possible common ratio and the first term? 3

Q: For which of the following series does the ratio test fail? 00 (e) None (a) k! k=1 (b) 2k (c) k=1k)…

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Q: For which of the following series does the ratio test fall? (e) None (a) (b) (c) (d)

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Q: . Find the values of p for which the series E=1 Inn is convergent. (with reason)

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Q: For what values of p is each series convergent? (-1)"-1 n=1 O P> -5 for any p except p= 0 O P<-5 for…

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Q: Approximate the value of the series to within an error of at most 10 4. (-1)"+1 n5 n=1 According to…

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Q: Find the interval of convergence for the given series. E (n + 7)!(x + 12)" n=0 Select the correct…

A: Let's find.

Q: Consider the following series. (x +9)" 5" Σ n=0 (a) Find the values of x for which the series…

A: b) Given:                ∑n=0∞x+9n5n             =∑n=0∞x5+95n     It is an infinite geometric series…

Q: For what value/values of x does the series 2(- 1)" x" converges? n =0

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Q: The sum of the series E 4(5)" is n n=0

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Q: Make up a geometric series E infinity/ n=1 ar^n-1 that converges to the number 5 for the following…

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Q: (-1)" For the series En=1 n3 00

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Q: (a) For what values of x is the following series convergent? Σ 00 n=0 (b) Find the value of x that…

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Q: ) For what values of x do the following power series converge? G(r) = (* - 2)" n5" n=1

A: By the ratio test Let an =(x-2)n/(n5n)      |an+1|/|an| =|(x-2)n+1/((n+1)5n+1)|/|(x-2)n/(n5n)|…

Q: For what values of p is the series convergent? ∞ Σ(−1)n-1 (Inn)² n=2 n³

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Q: For which of the following series does the ratio test fail? 1 (e) None (b) (c) (d) k! (k +1)! k=1

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Q: 1 Use the identity S y" to express the function as a geometric series in the indicated term. 1 - y n…

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Q: (х — 10)" 00 10" n=1 WI

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Q: 4. For which of the following series is the Ratio Test inconclusive? (Note: there could be more than…

A: We have to identify which series inconclusive by ratio test

Q: 92'e dr 1. ermine whether the following series converges or 9n'e n

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Q: Find all the values of x such that the given series would converge. (x - 6)" 6" n=1

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Q: (a) For what values of x is the following series convergent? 00 enx n=0 (b) Find the value of x that…

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Q: what values

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Q: Consider the following geometric series. Σ (-2)" – 1 n = 1 Find the common ratio. Trl %3D 8

A: Given, The geometric series  ∑n=1∞-2n-17n We have to find the common ratio.

Q: For which of the following series is the Ratio Test inconclusive? Select one: Σ Σ * (-3)* +1 n=1…

A: To find for which series the Ratio test is inconclusive.

Q: For what values of p is each series convergent? (-1)"-1 n=1 O P> -2 O P<-2 for all p P< -2 for any p…

A: We have to check

Q: Find all the values of x such that the given series would converge. (x – 3)" | 3" n=1

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Q: he convergence or divergence of the given series or state tha 1 10 n=

A: Answer is convergent.

Q: Find the first five terms of a power series for e*. +4

A: This question is based on power series expansion of ex.

Q: What can we conclude from applying the Ratio Test to the following series? E(-3)"n-1/2. n=1

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Q: For what values of p and q does the following series converge? Με n=2 1 nP(Inn)a

A: Consider the series ∑n=0∞1np The series is convergent if p&gt;1. Note: ln n&lt;n for n is a positive…

Q: (x – 9)" - 9" n=1

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Q: (b) For which real values of does each of the following series converge? Justify your answer. kkk 1.…

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Q: For what values of p does the following series converge? (In n) 9 n-2 PS-10 P<-10 p< 8 p2-12 PS8

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Q: For which of the following series does the ratio test fail? 8, (a) 1 k (b) (e) None k! (c) (d) k!…

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Q: Find the sum of the given series. E[1+ (-1)*] = i=1

A: To find the sum of the below series. ∑i=161+−1i

Q: 3. a) Use the sum of the first 10 terms to estimate the sum of the given series. n-1 b) Improve this…

A: We have to find the sum and improve the estimates.

Q: Find the values of x for which the given geometric series converges. Also, find the sum of the…

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Q: For what values of p is this series convergent? s(-1)" - 1 nP + 3 O p> -3 O p2 -3 O for all p O p +…

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Q: Find all the values of x such that the given series would converge. (5)" (/n + 6) n=D1

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Q: The following series: Σ * 36 n2 1 n=2 Expressed as a telescopic series or a sum of two telescopic…

A: The given series is:∑n=2+∞36n2-1

Q: M M For which of the following series does the ratio test fall? (e) None k (b) kk 1. (a) (c) (d) 3k…

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Q: For what values of x does the series E-1 n=1 x21+3 12² converge?

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Q: For which of the following series does the ratio test fail? (e) None (k + 1)! a b C d e

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Q: For which values of x does the given series converge? E (n + 2)! x" n=0

A: ANSWER IS OPTION (b)  x=0

Q: for what value of x do the following power ?series converge Σ En!x" : n=0

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Q: Use the test of your choice to determine whether the following series converge.

A: Given: ∑k=1∞ 15k-1 To determine: Given series is convergent or divergent.

Q: Consider the following. 12 Σ n(n + 3) n = 1 (a) Find the sum of the series. Sn x

A: Given series is ∑n=1∞12nn+3

Q: 4. Calculate the sum of the S series with an accuracy 0.001. 1 S 23

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Q: The value of p for the series En=1 2n | n! by using ratio test is

A: Given series is ∑n=1∞2nn! According to the ratio test a series is convergent if in the limit…