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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


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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
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If  is decreasing and bounded, then 

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

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Sequences And Series Of Real Numbers -6 - Question 3
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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
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is bounded and bn —> 0, choose the appropriate conclusion from the following options
Sequences And Series Of Real Numbers -6 - Question 5
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The value of x for which of the following series converges is
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Sequences And Series Of Real Numbers -6 - Question 6
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Detailed Solution for Sequences And Series Of Real Numbers -6 - Question 6



Sequences And Series Of Real Numbers -6 - Question 7
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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
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The sequence {1, 0,1, 0,1, 0,...} is
Sequences And Series Of Real Numbers -6 - Question 9
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The sequence {xn}, where xn = converge to
Sequences And Series Of Real Numbers -6 - Question 10
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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
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If the sequence be defined by a1 = 1 and an+ 1 =  is equal to
Sequences And Series Of Real Numbers -6 - Question 12
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  converges to a, for all n, a ≥  0, then 
Sequences And Series Of Real Numbers -6 - Question 13
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  then the sequence {xn} converge to
Sequences And Series Of Real Numbers -6 - Question 14
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What is true for the sequence given by an 
Sequences And Series Of Real Numbers -6 - Question 15
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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
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The sequence {xn}, where xn  converge to
Sequences And Series Of Real Numbers -6 - Question 17
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The sequence {xn}, where xn  converges to
Sequences And Series Of Real Numbers -6 - Question 18
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 then the sequence {xn} converge to the positive root of the equation 
Sequences And Series Of Real Numbers -6 - Question 19
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The sequence { xn } , where xn =  converge to 
Sequences And Series Of Real Numbers -6 - Question 20
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A sequence {an} may be defined by a recursion formula
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