All Courses
Get the App Signup / Login
Sign in Open App
Mathematics Exam  >  Mathematics Tests  >  Topic-wise Tests & Solved Examples for Mathematics  >  Sequences And Series Of Real Numbers -6 - Mathematics MCQ

Sequences And Series Of Real Numbers -6 - Mathematics MCQ


Test Description

20 Questions MCQ Test Topic-wise Tests & Solved Examples for Mathematics - Sequences And Series Of Real Numbers -6

Sequences And Series Of Real Numbers -6 for Mathematics 2024 is part of Topic-wise Tests & Solved Examples for Mathematics preparation. The Sequences And Series Of Real Numbers -6 questions and answers have been prepared according to the Mathematics exam syllabus.The Sequences And Series Of Real Numbers -6 MCQs are made for Mathematics 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Sequences And Series Of Real Numbers -6 below.
Solutions of Sequences And Series Of Real Numbers -6 questions in English are available as part of our Topic-wise Tests & Solved Examples for Mathematics for Mathematics & Sequences And Series Of Real Numbers -6 solutions in Hindi for Topic-wise Tests & Solved Examples for Mathematics course. Download more important topics, notes, lectures and mock test series for Mathematics Exam by signing up for free. Attempt Sequences And Series Of Real Numbers -6 | 20 questions in 60 minutes | Mock test for Mathematics preparation | Free important questions MCQ to study Topic-wise Tests & Solved Examples for Mathematics for Mathematics Exam | Download free PDF with solutions
Sequences And Series Of Real Numbers -6 - Question 1
Save

If  is decreasing and bounded, then 

Sequences And Series Of Real Numbers -6 - Question 2
Save

The sequence {xn}, where 

Detailed Solution for Sequences And Series Of Real Numbers -6 - Question 2

If a sequence is eventually increasing and not bounded above, then it is divergent to positive infinity. If a sequence is eventually decreasing and not bounded below, then it is divergent to negative infinity.

1 Crore+ students have signed up on EduRev. Have you? Download the App
Sequences And Series Of Real Numbers -6 - Question 3
Save

The sequence {xn}, where 

Detailed Solution for Sequences And Series Of Real Numbers -6 - Question 3

as  it is a gp so as n increase sum will be more  
xn = a(rn-1)/(r-1)
xn = (1)(1/2n-1)/(1/2-1)
xn will be terminating 

Sequences And Series Of Real Numbers -6 - Question 4
Save

is bounded and bn —> 0, choose the appropriate conclusion from the following options
Sequences And Series Of Real Numbers -6 - Question 5
Save

The value of x for which of the following series converges is
Detailed Solution for Sequences And Series Of Real Numbers -6 - Question 5

Sequences And Series Of Real Numbers -6 - Question 6
Save

Detailed Solution for Sequences And Series Of Real Numbers -6 - Question 6



Sequences And Series Of Real Numbers -6 - Question 7
Save

Suppose (cn) is a sequence of real numbers such that |cn|1/n exists and is non-zero. If the radius of convergence of the power series cn xn is equal to r, then the radius of convergence of the power series n2cnxn is
 
Detailed Solution for Sequences And Series Of Real Numbers -6 - Question 7

Radius of convergence = R =
⇒ R = r
So radius of convergence of is
R1 = 
⇒ r.1 = 1
 

Sequences And Series Of Real Numbers -6 - Question 8
Save

The sequence {1, 0,1, 0,1, 0,...} is
Sequences And Series Of Real Numbers -6 - Question 9
Save

The sequence {xn}, where xn = converge to
Sequences And Series Of Real Numbers -6 - Question 10
Save

Let an = least power of 2 that divides n. For instance, a1 = 0, a2 = 1, a3 = 0, a4 = 2. Then, the sequence <an> is
Detailed Solution for Sequences And Series Of Real Numbers -6 - Question 10

 The correct answer is Option 2: diverging to infinity. Explanation: The sequence starts with 0, 1, 0, 2, 0, 1, 0, 3, ... and so on. We can observe that the sequence is not bounded because it keeps increasing with each term. The sequence does not converge to a specific number either. Instead, it keeps diverging to larger and larger powers of 2 as n increases. Therefore, the correct answer is that the sequence is diverging to infinity

Sequences And Series Of Real Numbers -6 - Question 11
Save

If the sequence be defined by a1 = 1 and an+ 1 =  is equal to
Sequences And Series Of Real Numbers -6 - Question 12
Save

  converges to a, for all n, a ≥  0, then 
Sequences And Series Of Real Numbers -6 - Question 13
Save

  then the sequence {xn} converge to
Sequences And Series Of Real Numbers -6 - Question 14
Save

What is true for the sequence given by an 
Sequences And Series Of Real Numbers -6 - Question 15
Save

Which one of the following is false?
Detailed Solution for Sequences And Series Of Real Numbers -6 - Question 15


finite and non = zero

By the comparison test, both the series ∑un & ∑vn

converges and diverges together. Since, ∑1/n is divergent, therefore is also divergent.

Sequences And Series Of Real Numbers -6 - Question 16
Save

The sequence {xn}, where xn  converge to
Sequences And Series Of Real Numbers -6 - Question 17
Save

The sequence {xn}, where xn  converges to
Sequences And Series Of Real Numbers -6 - Question 18
Save

 then the sequence {xn} converge to the positive root of the equation 
Sequences And Series Of Real Numbers -6 - Question 19
Save

The sequence { xn } , where xn =  converge to 
Sequences And Series Of Real Numbers -6 - Question 20
Save

A sequence {an} may be defined by a recursion formula
27 docs|150 tests
Join Course
Information about Sequences And Series Of Real Numbers -6 Page
In this test you can find the Exam questions for Sequences And Series Of Real Numbers -6 solved & explained in the simplest way possible. Besides giving Questions and answers for Sequences And Series Of Real Numbers -6, EduRev gives you an ample number of Online tests for practice
Download as PDF

Important Questions for Sequences And Series Of Real Numbers -6

Find all the important questions for Sequences And Series Of Real Numbers -6 at EduRev.Get fully prepared for Sequences And Series Of Real Numbers -6 with EduRev's comprehensive question bank and test resources. Our platform offers a diverse range of question papers covering various topics within the Sequences And Series Of Real Numbers -6 syllabus. Whether you need to review specific subjects or assess your overall readiness, EduRev has you covered. The questions are designed to challenge you and help you gain confidence in tackling the actual exam. Maximize your chances of success by utilizing EduRev's extensive collection of Sequences And Series Of Real Numbers -6 resources.

Sequences And Series Of Real Numbers -6 MCQs with Answers

Prepare for the Sequences And Series Of Real Numbers -6 within the Mathematics exam with comprehensive MCQs and answers at EduRev. Our platform offers a wide range of practice papers, question papers, and mock tests to familiarize you with the exam pattern and syllabus. Access the best books, study materials, and notes curated by toppers to enhance your preparation. Stay updated with the exam date and receive expert preparation tips and paper analysis. Visit EduRev's official website today and access a wealth of videos and coaching resources to excel in your exam.

Online Tests for Sequences And Series Of Real Numbers -6 Topic-wise Tests & Solved Examples for Mathematics

Practice with a wide array of question papers that follow the exam pattern and syllabus. Our platform offers a user-friendly interface, allowing you to track your progress and identify areas for improvement. Access detailed solutions and explanations for each test to enhance your understanding of concepts. With EduRev's Online Tests, you can build confidence, boost your performance, and ace Sequences And Series Of Real Numbers -6 with ease. Join thousands of successful students who have benefited from our trusted online resources.
© EduRev
Education Revolution
Follow Us
Signup to see your scores go up
within 7 days!
Takes less than 10 seconds to signup