Problem #7:Determine the convergence or divergence of the series >n=1Problem #7:(A) The series is absolutely convergent (B) There is not enough information to determine(C) The series is divergent (D) The series is conditionally convergentSelect(-1)-¹(n+914)Save

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Answered: Problem #7: Determine the convergence…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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4. Determine if the series is absolutely convergent, conditionally convergent, or divergent using one of the following (divergence test, integral test, comparison test, limit comparison test, alternating series test, ratio test, root test).
An environmental engineer wants to evaluate three different methods for disposing of nonhazardous chemical waste: land application, fluidized-bed incineration, and private disposal contract. Use the estimates below to help her determine which has the least cost at /= 15.00% per year on the basis of an annual worth evaluation. First Cost AOC per Year Salvage Value Life Land $-145000 $-86000 $23000 4 years Incineration $-760000 $-70000 $260000 6 years Contract O $-132000 O 2 years
12. Determine if the series is absolutely convergent, conditionally convergent, or divergent using one of the following (divergence test, integral test, comparison test, limit comparison test, alternating series test, ratio test, root test).
7. Evaluate the series (-2)k+1 32k-1 k=2 8 8 2 3 3 (a) (b) 21 33 9 6 6 4 (e) (f) 7 11 (i) The series is convergent, but not equal to any of these answers. 8 45 (h) 4 (j) The series is divergent. (d)
Problem 1. The Alternating Series Test states that if the positive sequence {b„} is (1) decreasing, and (2) convergent to 0, then the series > (-1)"+'bn converges. But what if we drop the assumption that {bn} is decreasing? Is the n=1 result still true? Consider the series defined by 1 1 1 1 1 1 1 1 (-1)"+1bn, - 2 4 3 8. 4 16 2n n=1 where the sequence b, is defined by 1 1 1 1 1 1 1 4' 3'8'4'16’5'32' 1 1 } n 2n (a) Does this sequence {bn} satisfy the assumptions of the Alternating Series Test? Which does it satisfy, and which does it fail? 1 (b) Show that this series diverges. (Hint: This series can also be written as Suppose that it did n 2n n=1 should converge. If you add a certain geometric series to it, you're adding two convergent series together, so you get another convergent series but do you?) (c) Is the Alternating Series Test wrong? Explain why not.
For problem 2 part 2: To get your comparison series for LCT, choose the series with leading term over leading term. So you want the series of sqrt{n} over n "leading term over leading term" then go from there
Problem 2: Consider the series >(-1)"- Does this series converge or diverge? If you are using a test for convergence/divergence, make sure to clearly show that the conditions of the test are met. n=1 en
13) The integer n = a) If n = 3 (mod 9), then what is x ? b) If n = 3 (mod 11), then what is x ? Hint for #13: 12700140x3243243 is missing the digit x. Consider the number 1234. By writing each digit in scientific notation, we have 1234 1 x 10³ +2× 10² +3 × 10¹ + 4 × 10⁰ Then notice that 10 = 1 (mod 9). When we reduce mod 9, we obtain 1234 1 x 10³ +2× 10² +3 x 10¹ + 4 x 10⁰ = = 1x 1³ + 2 x 1² + 3 × 1¹ + 4 × 1⁰ = 1+ 2+ 3+ 4 = 10 = 1 (mod 9). Since 10 = -1 (mod 11), when we reduce mod 11, we obtain 1234 1 x 10³ +2× 10² +3 x 10¹ + 4 x 10⁰ = = 1x (-1)³ +2× (-1)² +3 × (-1)¹ +4× (-1)⁰ = -1 + 2-3 + 4 = 2 (mod 11).
1. If the series an is convergent and an > 0 for all n, then we also know that n=1 (a) Must be Convergent (b) Must be Divergent (c) Can be either Convergent or Divergent, depending on an M8 n=1 an n E
∞ 1. Let an be a POSITIVE infinite series (i.e. an > 0 for all n ≥ 1). Let ƒ be a continuous function n=1 with domain R. Is each of these statements true or false? If it is true, prove it. If it is false, prove it by providing a counterexample and justify that is satisfies the required conditions.
AQuestion Completion Status: Problem 1: Which of the following series converge by the alternating series test. Select all that apply. (-1)"n² 回》 Vn3 + 1 n=1 8 [ii] (-1)"-!el-n n=1 (-1)" [iii] ) 2+3n n=1 [iv] (-1)"n In(n) n=1 [i] [ii] [iv] Save All Answers Close Window Click Save and Submit to save and submit. Click Save All Answers to save all answers. pg.jpg MATH1132_Q11.2.pdf pg.jpg MATH1132_Q11.4.pdf MATH1132_Q11.3.pdf Essay 1 Makin....docx POF MacBook Pro
PART V: (a) Show that the following series converges conditionally. E-1)+1_n² n° +2 (b) Find an estimate for the error in approximating the series by the sum of its first five terms, then find an estimate for the sum of the series.

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Problem #7: Determine the convergence or divergence of the series > n=1 Problem #7: (A) The series is absolutely convergent (B) There is not enough information to determine (C) The series is divergent (D) The series is conditionally convergent Select (-1)-¹(n+914) Save