Explain why or why not Determine whether the following state- ments are true and give an explanation or counterexample. a. The sum E 34 is a p-series. 1 is a p-series. b. The sum Vk - 2 k=3 c. Suppose f is a continuous, positive, decreasing function, for x 2 1, and a, = f(k), for k = 1, 2, 3, . ... If Ea k=1 converges to L, then , f(x) dr converges to L. d. Every partial sum S, of the series z underestimates the =1 k exact value of > e. If EkP converges, then EkP+0.001 f. If lim az = 0, then az converges. converges. k

Q: 3. Decide whether each or not of the following series converges. k?7k (а) Σ (k + 1)4k* k=0

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Q: 2. Determine whether the following series are absolutely convergent or not. ( a ) Σ * (-1)" m=1 3n…

A: Explanation of the answer is as follows

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Q: For which value of p the series E n(1+n²Y converges. O ps-2 O p<2 O p22 O p2-2

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Q: 3. Decide whether each or not of the following series converges. Σ k(-2)* 52k-1(k+1)!" (b) k=0

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Q: Find the smallest value of x for which the series Σ (x+101)" 2ln(n) n=2 is conditionally convergent.

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Q: (a) For which numbers x does the geometric series E(3x – 2)" converge? (b) To what does the above…

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Q: For which value of p the series n(1 + n converges. ps-2 p22 p2-2 p<2

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Q: 3. Decide whether each or not of the following series converges. (k + 1)4* * k=0 k(-2)* と2k-1(k +1)!…

A: To decide whether each of the following series convereges or not.

Q: Which of the following is a convergent series? 1 n=1 1 nyInn n=2 00 2" n3 n= 00 n" n! n=1

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Q: For which positive integers k is the following series convergent? 8. (kn)! n = 1 k ? 0

A: Series and sequences, ratio test

Q: Which of the following is a convergent series? O 00 1 L nyn O 00 1. n2 nvlnn O n"

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

Q: 1. Which of the following is a convergent p-series? (A) n³ n=1 n (B) 3 n=1 1 (C) n=1 3 1 (D) n n=1

A: A) ∑n=1∞ n3     Since n is positive integer⇒  The above series diverges B) ∑n=1∞13n   It is not p…

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Q: Decide whether or not the following numerical series converge. 1 + 4* . 5-2k 1 (c) k + 3 k + 2" k=0…

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Q: For what values of x does the series converge conditionally? gn xn Σ n! n=1 None x=-1/8 x=0 x=1/8

A: This question is based on series and convergance concept

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Q: 1. Use any method to determine whether the following series converges or dive (a) E(-1)" n=1 (-1)"+1…

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Q: Find all the values of x such that the given series would converge. 00 5 11"(x")(n+ 1) (n + 4) n=1

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Q: For what values of x does the series converge conditionally? gn xn n! n=1 x=1/8 x=0 None X=-1/8

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Q: For what values of x are the following series convergent? x" Σ п(п + 1) (c) n=1 00 n2 (d) E ith 1+…

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Q: 1. Determine whether each of the following series converges or diverges. 00 1 A. E n(In(n))³ n=2

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A: We have to find the sum of the infinite series ∑n=1∞31n-31n+1.

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Q: Decide whether or not the following numerical series converge. (-3)k+1k2 k!(k + 2) (b) k=0 3.

A: Apply Alternating series testt

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

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

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Q: Given the following series: 00 (п + 1)x2п-1 3" n=0

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Q: 8"х" (п + 1) Σ п+ 10 n=1

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Q: 1. Use any method to determine whether the following series converges or diverges. (a) E(-1)" 5 n=1…

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Q: Determine whether the following series are absolutely convergent: ( a) Σ-)"-1 (b) E(-1)7-11·3.…...·…

A: Here the given series is  a∑n=1∞-1nnn+1b∑n=1∞1n-11·3···2n-12n-1!

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Q: Which of the following is a convergent p-series? 3 A) 2 n=1 n 3 n=1 1 n=1 3 D n=1

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Q: Find the smallest value of x for which the series (x + 46)" 2'n(n) is conditionally convergent.…

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Q: Find the radius and interval of convergence of the following series. n +1 7n=1

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Q: Which of the following is a convergent p-series? Select all that apply. 1 n =1 7" 4 Σ n =1 n? 2 E…

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