8. Which of the series converge, and which diverge?:n +1(a)n² /n1(c)1+ In²n(In n)?(d)n311(e)nn! Inn(f)n(п+2)!n!(g)n"(n!)"(h)(n")²1.3.5..(2n – 1)(i)(2.4.(2n)I(3" + 1)8W-8W-8W-8W-8W•8W-8W-

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Answered: 8. Which of the series converge, and…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Consider the three infinite series below. • (-1)-1 (n+1) (, 1) (11) Sn 4n³-2n +1 #=1 #=1 (a) Which of these series is (are) altemating? (b) Which one of these series diverges, and why? (c) One of these series converges absolutely. Which one? Compute its sum. n=1 5(-4)"+2 32n+1
10. Find all values of a for which the following series converge. n2(n + 2) (n + 5)3n (2) Σ n=l 72 (1+x²)n (b) n=l (0) Σ n=1 2n + 3n na -(2x + 1)"
(12) Consider the three infinite series given below: (-1)"-1 ř (n+1)(n²–1) ii) E 4n° – 2n +1 10(2)**2 32n+1 i) E 5n iii) n=1 n=1 n=0 a) Which one of these series diverges? Justify your answer. b) Identify the alternating series and verify that it converges. c) One of these series has a sum that may be computed; find the sum of this series.
Which of the three series (i) (- 1)n -1 cos(n) (ii) E (-1)n-1 M (-1)n -1 In(n) (ii) n= 1 7n n= 1 n=2 is conditionally convergent?
Evaluate the infinite series by identifying it as the value of an integral of a geometric series. (– 1)" 87 +1(n + 1) 2 In (3) x n=0 1 n+1 |f(t)dt se)dt where f(=) = (- )"(;) 1 x" = Hint: Write it as 8 8 + x n=0

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8. Which of the series converge, and which diverge?: n+1 (2) Σ S 3 (c) 1 1 + ln²n (Inn)² n³ (d) n 1 (Ⓒ) (² - -/- )* n n! In n n(n + 2)! (f) (g) (h) (i) 8-8-8-8-88- Σ (n!)n (nn)² 1.3.5..... (2n-1) · [2.4......(2n)](3¹ + 1)