1. Prove that the following series is convergent for all r ER E(1 + 1 1 sin(nr) ... n. n=1

Q: Which of the following function has the Macularin series (-1)"4"" B. 1- x² C. A. 1 E. F. D. 1+ 4.72…

A: We will use basic knowledge of summations and Maclaurin series expansions to solve this question.

Q: Select all the convergent series a. Στη 1 b. n=1 C. ΣΤΑ 1 3" n! (-1)" n2

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Q: l x such that the

A: Here we have,  A=∑n=0∞(-3)nxnn+1=∑n=0∞an ⇒an=(-3)nxnn+1

Q: π Σn=13 + (-1)"+1n! Зе 3"

A: Ratio test: Suppose we have the series ∑n=0∞an Define, L=limn→∞an+1an. Then, (a) if L<1 the…

Q: Suppose that ho, hị, h2, . is a sequence defined as follows: ho = 1, h1 = 2, h2 = 3, %3D hy =…

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Q: A splnner with 6 equally slzed slices has 2 blue slices, 1 yellow slice, and 3 red slices. The dial…

A: The spinner has 6 equally sized slices. Of them, 2 are blue, 1 is yellow and 3 are red in colour.…

Q: Determine whether the following series is absolutely convergent using the Ratio Test. Show your work…

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Q: If |r| < 1, the series a +ar+ar² +...+arn−1 t... converges to

A: Series convergence.

Q: Which of the following series converges sin(n) n=0 (None 父 (– 1)"n n=0 n =on!

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Q: Let E an be an absolutely convergent series with an # 0 for all n. Show that sin(an) n=D1 is also…

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Q: Determine if the following series converge or diverge (n + 1)2 n(n+2)' (») Ž (b) E (a) VI+r? n=1 2.

A: In the given question we have to check the convergence and divergence of the given two series. for…

Q: 2. Use ratio test to determine whether the following series is convergent or divergent: (2n)! Σ n.…

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Q: Find if the series converges or divereges.

A: The answer is given below.Explanation:

Q: Which of the following series converge absolutely? a. (-1)" Σ n3 n=1 n=1 00 C. (-1)" Σ Vn n=1 b.

A: To find the Absolute Convergence of the given series.

Q: 9.. For the series 1+n² a. Show that the series passes the divergence test (nth term test). b. Apply…

A: The given series is ∑n=1∞n1+n2. (a) To Show: this series passes the divergence test. (b) To Show:…

Q: Which of the following series converges absolutely, conditionally, and which diverges? A) E(-1y 3+n…

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Q: For what values of x does the series, (-1)"(3 – x)" n4n n=1 a) absolutely, b) conditionally?

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Q: E(-1)" cos (1/n²) COS

A: Alternating Series: An infinite series of the form ∑-1n-1un whose terms are alternatively positive…

Q: а) nyn n=1 Σ >(-1)n+1 п c) 2" n=1 00 e) 2(-1)n+1, en n=1

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Q: State whether ths series converges absolutely, conditionally, or diverges

A: We have given series- We have to find if the given series converges absolutely, conditionally, or…

Q: Cos 3n (g) Σ 1+(1.2)" n=1 n n2n (h) Σ (1+ 2n²)n n=1

A: Determine whether each of the following series is convergent or divergent using the appropriate test…

Q: Find the interval of the values of x for which the following series converges: 00 n! n=1 The above…

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Q: cos Σ 1+1 Consider the series n n=174 O It converges absolutely. O It converges conditionally. O It…

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Q: Q.2\Prove the Maclaurin series: (-1)"-1xn In(1+ x) = En=1' ,-1<x<1.

A: We have to prove maclaurin series.

Q: Which of the following series converges and which diverges? A) Š Vn n=2 Inn Ans. Diverges ( n"-term…

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Q: Which of the following series converges absolutely, conditionally, and which diverges? A)…

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Q: Which of the following series is converge, and which diverge? (2n)! d) En-o(-1)". 2n nin

A: ∑n=1∞-1n2n!2nn!n

Q: When the ratio test is applied on the power series > Cn(x – 4)", the resulting limit is Which of n=0…

A: Here we use ratio test formulas.

Q: Prove that the following series is convergent for all r E R sin(nr) + n. п n=1

A: