13. Does the series X∞ n=0 (−1)n 1 √ n2 +1 converge absolutely, converge conditionally, or diverge? Answer: The terms √ 1 n2+1 are decreasing and go to zero (you should check this), so the Alternating Series Test says that the series converges. To see that the series does not converge absolutely, it suffices to show that the series X∞ ...
Question 4 (***+) An arithmetic series has common difference 2. The 3rd, 6th and 10 th terms of the arithmetic series are the respective first three terms of a geometric series. Determine in any order the first term of the arithmetic series and the common ratio of the geometric series. MP2-Z , a =14 , 4 3 r =
Both series converge by the AST since a n= 1 n+1 is positive, decreasing and converges to 0. In conclusion, the radius of convergence is R= 3 and the interval of convergence is [2,7] . (b)Find f(7)(4), f(8)(4) and f(9)(4). Solution. Since the given series must be the Taylor series of fat a= 4, the coefficient of (x−4)7 in the series is f(7)(4) 7!
8. Find the sum of the arithmetic series. 17 + 27 + 37 +...+ 417. 9. An arithmetic series has five terms. The first term is 2 and the last term is 32. Find the sum of the series. 10. In an arithmetic sequence, the first term is –2, the fourth term is 16, and the E!" term is 11 998. (a) Find the common difference d. (b) Find the value of n. 11.
The fourth term of a geometric series is 10 and the seventh term of the series is 80. For this series, find (a) the common ratio, (2) (b) the first term, (2) (c) the sum of the first 20 terms, giving your answer to the nearest whole number. (2) Jan 08 Q2 6. A geometric series has first term 5 and common ratio 5 4
Sequences and Series Exam Questions - Free download as PDF File (.pdf), Text File (.txt) or read online for free. The document is a study guide for sequences and series for Grade 12. It includes exercises on arithmetic sequences and series, geometric sequences and series, and past exam questions. The exercises cover topics such as determining terms, common differences, sums of sequences ...
Evaluate the series (n — A) -18 B) D) 21 D) 39 D) 121 D) 756 Evaluate the series B) the series I + 3 9 + 27 + 81 + 243. B) 363 A) 364 What is the sum of the geometric series A) 15,658 B) 6,138 Does the infinite geometric series diverge or converge? Explain. 3 6 12 24 A) It diverges; it has a sum. B) It diverges; it does not have a sum. 16 ...
16) Decide which infinite geometric series has a sum. a. ½ – 1 + 2 – 4 + … b. 64 + 48 + 36 + 27 + … c. d. 16 – 20 + 25 – 21.25 + … Evaluate the infinite geometric series, if possible. 17) 18) Solve the given problems. 19) An auditorium contains 10 seats in the first row, 12 seats in the second, 14 in the third, and so on.
Sequence and Series Questions and Answers PDF for free download for SSC CGL, CHSL Competitive exams. Previous year exam fully solved MCQs with detail explanation for preparation of Mathematics for upcoming examinations. What is a Sequence and Series? a) A series of events occurring in chronological order
18 CHAPTER 10. SEQUENCES AND SERIES Since finite sums and limits are both linear, so are series. Theorem 10.3.2 (Linearity of Series). Assume the following series are convergent, then åcan = cåan, and å(an +bn) = åan +åbn. We can now return to the example from the previous page and a similar example. ¥ å n=0 1 +( n2) 32n ¥ å n=0 3n ...
Number Series Questions with Answers at SmartKeeda. Download PDFs and take free quiz tests to enhance your expertise in Number Series. Boost your knowledge today! Join Testzone. ... Yes, number series questions can appear in a variety of exams and assessments, including IBPS PO Pre, SBI PO Pre, LIC Assistant, SBI Clerk, IBPS Clerk, LIC AAO ...
Question: 1. In each of the following questions, one number is missing in the series. You have to understand the pattern of the series and insert the number. 16, 22, 34, 58, 106, ….., 394 (A) 178
n, and called a series.Theseriesconverges is the sequence F s n k of partial sums converges. Otherwise, the series diverges. If lim n→∞ s n = s,we write 3∞ n=1 a n = s and call s the sum of the series. Example. Consider the geometric series 3∞ n=0 arn = a+ar +ar2 +...,wherea and r are constants. It is divergent if |r| ≥1. It is ...
Sequences and Series – CHAPTER 8 243 The sequence has a first term of 5. Enter this and press ENTER or EXE. The common difference of the sequence is 7 so enter + 7. The display will show Ans + 7 which means ‘add 7 to the previous answer. From here, every time you press ENTER (or EXE), you will repeat the calculation, generating successive ...
7 Sequences and series 215 Short questions 1. Th e fourth term of an arithmetic sequence is 9.6 and the ninth term is 15.6. Find the sum of the fi rst nine terms. [5 marks] 2. Th e sum of the fi rst n terms of a series is given by: S n = 2n2 – n, where n ∈ +. (a) Find the fi rst three terms of the series.
Number Series and Alphabets (Letter) Series Questions PDF for SSC CGL, CHSL, Competitive Exams for free download. Number Series and Alphabets Series Questions . ... Answer : (4) 625, 3125, 15625. Directions : In each of the following questions, a series is given, with one term missing. Choose the correct alternative from the given ones that ...
Number Series Questions PDF Set 2 - Free download as PDF File (.pdf), Text File (.txt) or read online for free. The document presents 50 number series questions with multiple choice answers. It tests the ability to recognize patterns in numeric sequences and determine the next number in the series. The correct answers are provided at the end for verification.
Number Series Questions and Answers PDF: Series is a sequential arrangement of numbers in number series questions and answers pdf, where each term in the series is obtained in accordance with a set of rules. Mathematical operations including addition, subtraction, multiplication, division, square roots, cube roots, and others can serve as the ...
Verbal Reasoning Number Series, Alphabet, Letter Completion Questions and Answers Pdf Download for various Competitive Exams and Entrance Mock-Online Test. - 1
