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Mathematics Exam  >  Mathematics Tests  >  Topic-wise Tests & Solved Examples for Mathematics  >  Sequences And Series Of Real Numbers -9 - Mathematics MCQ

Sequences And Series Of Real Numbers -9 - Mathematics MCQ


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20 Questions MCQ Test Topic-wise Tests & Solved Examples for Mathematics - Sequences And Series Of Real Numbers -9

Sequences And Series Of Real Numbers -9 for Mathematics 2024 is part of Topic-wise Tests & Solved Examples for Mathematics preparation. The Sequences And Series Of Real Numbers -9 questions and answers have been prepared according to the Mathematics exam syllabus.The Sequences And Series Of Real Numbers -9 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 -9 below.
Solutions of Sequences And Series Of Real Numbers -9 questions in English are available as part of our Topic-wise Tests & Solved Examples for Mathematics for Mathematics & Sequences And Series Of Real Numbers -9 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 -9 | 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 -9 - Question 1
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The series is

Detailed Solution for Sequences And Series Of Real Numbers -9 - Question 1


By Ratio's Test, we have
If Then series is convergent
If Then series is divergent
If x = 1, The Ratio's Test fails.

If x = 1, then series becomes

finite and non – zero

By comparison test, both the series converge

and diverges together since ∑ 1/n2 in convergent, therefore is convergent. 

Sequences And Series Of Real Numbers -9 - Question 2
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The series  converges, if

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Sequences And Series Of Real Numbers -9 - Question 3
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 then the sequence {xn} converges to 

Sequences And Series Of Real Numbers -9 - Question 4
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 is equal to
Sequences And Series Of Real Numbers -9 - Question 5
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A school has four sections of chemistry in class XII having 40, 35, 45 and 42 students. The mean marks obtained in chemistry tests are 50, 60, 55 and 45 respectively for the four sections, the overall average of marks per student is
Detailed Solution for Sequences And Series Of Real Numbers -9 - Question 5

Total number of students = 40 + 35 + 45 + 42 = 162
Total marks obtained = (40 × 50) + (35 × 60) + (45 × 55) + (42 × 45) = 8465
Overall average of marks per student = 8465 / 162 = 52.25.

Sequences And Series Of Real Numbers -9 - Question 6
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If ∑an be the alternative series and ∑qn, ∑pn are series of negative and positive terms respectively if  ∑an is conditionally convergent, then
Sequences And Series Of Real Numbers -9 - Question 7
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A conditionally converges series is a series which is
Sequences And Series Of Real Numbers -9 - Question 8
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The series 
Sequences And Series Of Real Numbers -9 - Question 9
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 is equal to 
Sequences And Series Of Real Numbers -9 - Question 10
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If ai > 0 for i = 1, 2, 3,..,n and a1, a2, a3, ...an = 1 then the greatest value of (1 + a1)(1 + a2)... (1 + an) is:
Detailed Solution for Sequences And Series Of Real Numbers -9 - Question 10

2n

If ai > 0 for all i, then (1 + a1)(1 + a2)... (1 + an) > 1.

Since a1, a2, a3, ...an = 1, then (1 + a1)(1 + a2)... (1 + an) = (2)(2)...(2) = 2n.

Therefore, the greatest value of (1 + a1)(1 + a2)... (1 + an) is 2n.

Sequences And Series Of Real Numbers -9 - Question 11
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For real number a, if   converges to A and B respectively, then 
Sequences And Series Of Real Numbers -9 - Question 12
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then ∑an is 
Detailed Solution for Sequences And Series Of Real Numbers -9 - Question 12


Sequences And Series Of Real Numbers -9 - Question 13
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The series  converges, if
Sequences And Series Of Real Numbers -9 - Question 14
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Sequences And Series Of Real Numbers -9 - Question 15
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What is true about the geometric series 1 +r + r2 + ... (r > 0)?
Sequences And Series Of Real Numbers -9 - Question 16
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Let ∑un be a series of positive terms and let , then which among the following does not express the condition for the Cauchy’s nth root test?
Sequences And Series Of Real Numbers -9 - Question 17
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Which of the following series is alternating series?
Sequences And Series Of Real Numbers -9 - Question 18
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Let f(x) = (x – 2)17 (x + 5)24. Then
Detailed Solution for Sequences And Series Of Real Numbers -9 - Question 18

Here f(x) = (x – 2)17 (x + 5)24 
f17 (2) ≠ 0 
⇒ Odd derivative of function is non-zero. So, f has neither a minimum nor a maximum at 2.

Sequences And Series Of Real Numbers -9 - Question 19
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The domain of convergence for 1 + x + x2 + ... is
Sequences And Series Of Real Numbers -9 - Question 20
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Which of the following inequalities will be used in showing the serie  converges?
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