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Sequences And Series Of Real Numbers -8 - Mathematics MCQ


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19 Questions MCQ Test Topic-wise Tests & Solved Examples for Mathematics - Sequences And Series Of Real Numbers -8

Sequences And Series Of Real Numbers -8 for Mathematics 2024 is part of Topic-wise Tests & Solved Examples for Mathematics preparation. The Sequences And Series Of Real Numbers -8 questions and answers have been prepared according to the Mathematics exam syllabus.The Sequences And Series Of Real Numbers -8 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 -8 below.
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Sequences And Series Of Real Numbers -8 - Question 1

If for a given series  1; α, β ∈ R Then,

Sequences And Series Of Real Numbers -8 - Question 2

The series

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Sequences And Series Of Real Numbers -8 - Question 3

Which of the following series is absolutely convergent?

Sequences And Series Of Real Numbers -8 - Question 4

The series  is divergent, if

Sequences And Series Of Real Numbers -8 - Question 5

Let {an} and {bn} be sequences of real numbers defined as a1 = 1 and for n ≥ 1, an+1 = an + (–1)n 2–n, bn = . Then

Detailed Solution for Sequences And Series Of Real Numbers -8 - Question 5

Let {an} & {bn} be sequences of real numbers defined as a1 = 1



⇒ {bn} converges to 1.
Hence {bn} will be a Cauchy sequence.

Sequences And Series Of Real Numbers -8 - Question 6


Sequences And Series Of Real Numbers -8 - Question 7

 where m is a fixed positive integer is equal to 

Sequences And Series Of Real Numbers -8 - Question 8

Let ∑an be a convergent series of positive terms and let ∑bn be a divergent series of positive terms. Then,

Sequences And Series Of Real Numbers -8 - Question 9

The series 

Sequences And Series Of Real Numbers -8 - Question 10

The series 

Sequences And Series Of Real Numbers -8 - Question 11

Sequences And Series Of Real Numbers -8 - Question 12

Detailed Solution for Sequences And Series Of Real Numbers -8 - Question 12

Sequences And Series Of Real Numbers -8 - Question 13

Let ∑an be series o f real number and ∑pn and ∑qn be the series of positive and negative terms of ∑an respectively, then select the correct statement

Sequences And Series Of Real Numbers -8 - Question 14

Sequences And Series Of Real Numbers -8 - Question 15

Let {xn} be a sequence of positive terms, such that  does not exist, then

Sequences And Series Of Real Numbers -8 - Question 16

For which real number does the infinite series 

Sequences And Series Of Real Numbers -8 - Question 17

 is equal to 

Detailed Solution for Sequences And Series Of Real Numbers -8 - Question 17

Correct Answer:- A

Explanation : 

Sequences And Series Of Real Numbers -8 - Question 18

The series 1 + r + r2 + r3 + ... is oscillatory, if

Sequences And Series Of Real Numbers -8 - Question 19

Which of the following is absolutely convergent?

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