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Let {an}, {bn} and {cn} be sequences of real numbers such that bn = a2n and cn = a2n+1. Then {an} is convergent
- a)implies {bn} is convergent but {cn} need not be convergent
- b)implies {cn} is convergent but {bn} need not be convergent
- c)implies both {bn} and {cn} are convergent
- d)if both {bn} and {cn} are convergent
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
Let {an}, {bn} and {cn} be sequences of real numbers such that bn = a2...
If {an} is convergent, Then {bn} and {cn} both are convergent.
because {bn} and {cn} are sub sequence of {an}
because {bn} and {cn} are sub sequence of {an}
Most Upvoted Answer
Let {an}, {bn} and {cn} be sequences of real numbers such that bn = a2...
Introduction:
We are given three sequences of real numbers: {an}, {bn}, and {cn}. It is known that bn = a2n and cn = a2n-1. We need to determine the convergence of these sequences based on the given information.
Explanation:
To analyze the convergence of the sequences {an}, {bn}, and {cn}, we will consider the properties of each sequence individually.
Sequence {an}:
Since no information is provided about the convergence of {an}, we cannot conclude anything about its convergence based on the given information. Therefore, we cannot determine if {an} is convergent or not.
Sequence {bn}:
We are given that bn = a2n. This implies that every term in {bn} is the square of the corresponding term in {an}. If {an} converges, then the squares of its terms will also converge. Therefore, if {an} is convergent, {bn} will also be convergent.
Sequence {cn}:
We are given that cn = a2n-1. This implies that every term in {cn} is the product of a term in {an} and its preceding term. However, we cannot determine the convergence of {cn} based solely on this information. It is possible for {an} to be convergent while {cn} is not convergent. Therefore, we cannot conclude if {cn} is convergent or not.
Conclusion:
Based on the given information, we can conclude the following:
- The convergence of {an} cannot be determined.
- If {an} is convergent, then {bn} will also be convergent.
- The convergence of {cn} cannot be determined solely based on the given information.
Therefore, the correct answer is option 'C', which states that the convergence of both {bn} and {cn} cannot be determined based on the given information.
We are given three sequences of real numbers: {an}, {bn}, and {cn}. It is known that bn = a2n and cn = a2n-1. We need to determine the convergence of these sequences based on the given information.
Explanation:
To analyze the convergence of the sequences {an}, {bn}, and {cn}, we will consider the properties of each sequence individually.
Sequence {an}:
Since no information is provided about the convergence of {an}, we cannot conclude anything about its convergence based on the given information. Therefore, we cannot determine if {an} is convergent or not.
Sequence {bn}:
We are given that bn = a2n. This implies that every term in {bn} is the square of the corresponding term in {an}. If {an} converges, then the squares of its terms will also converge. Therefore, if {an} is convergent, {bn} will also be convergent.
Sequence {cn}:
We are given that cn = a2n-1. This implies that every term in {cn} is the product of a term in {an} and its preceding term. However, we cannot determine the convergence of {cn} based solely on this information. It is possible for {an} to be convergent while {cn} is not convergent. Therefore, we cannot conclude if {cn} is convergent or not.
Conclusion:
Based on the given information, we can conclude the following:
- The convergence of {an} cannot be determined.
- If {an} is convergent, then {bn} will also be convergent.
- The convergence of {cn} cannot be determined solely based on the given information.
Therefore, the correct answer is option 'C', which states that the convergence of both {bn} and {cn} cannot be determined based on the given information.
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Let {an}, {bn} and {cn} be sequences of real numbers such that bn = a2n and cn = a2n+1. Then {an} is convergenta)implies {bn} is convergent but {cn} need not be convergentb)implies {cn} is convergent but {bn} need not be convergentc)implies both {bn} and {cn} are convergentd)if both {bn} and {cn} are convergentCorrect answer is option 'C'. Can you explain this answer?
Question Description
Let {an}, {bn} and {cn} be sequences of real numbers such that bn = a2n and cn = a2n+1. Then {an} is convergenta)implies {bn} is convergent but {cn} need not be convergentb)implies {cn} is convergent but {bn} need not be convergentc)implies both {bn} and {cn} are convergentd)if both {bn} and {cn} are convergentCorrect answer is option 'C'. Can you explain this answer? for Mathematics 2024 is part of Mathematics preparation. The Question and answers have been prepared according to the Mathematics exam syllabus. Information about Let {an}, {bn} and {cn} be sequences of real numbers such that bn = a2n and cn = a2n+1. Then {an} is convergenta)implies {bn} is convergent but {cn} need not be convergentb)implies {cn} is convergent but {bn} need not be convergentc)implies both {bn} and {cn} are convergentd)if both {bn} and {cn} are convergentCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Mathematics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let {an}, {bn} and {cn} be sequences of real numbers such that bn = a2n and cn = a2n+1. Then {an} is convergenta)implies {bn} is convergent but {cn} need not be convergentb)implies {cn} is convergent but {bn} need not be convergentc)implies both {bn} and {cn} are convergentd)if both {bn} and {cn} are convergentCorrect answer is option 'C'. Can you explain this answer?.
Let {an}, {bn} and {cn} be sequences of real numbers such that bn = a2n and cn = a2n+1. Then {an} is convergenta)implies {bn} is convergent but {cn} need not be convergentb)implies {cn} is convergent but {bn} need not be convergentc)implies both {bn} and {cn} are convergentd)if both {bn} and {cn} are convergentCorrect answer is option 'C'. Can you explain this answer? for Mathematics 2024 is part of Mathematics preparation. The Question and answers have been prepared according to the Mathematics exam syllabus. Information about Let {an}, {bn} and {cn} be sequences of real numbers such that bn = a2n and cn = a2n+1. Then {an} is convergenta)implies {bn} is convergent but {cn} need not be convergentb)implies {cn} is convergent but {bn} need not be convergentc)implies both {bn} and {cn} are convergentd)if both {bn} and {cn} are convergentCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Mathematics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let {an}, {bn} and {cn} be sequences of real numbers such that bn = a2n and cn = a2n+1. Then {an} is convergenta)implies {bn} is convergent but {cn} need not be convergentb)implies {cn} is convergent but {bn} need not be convergentc)implies both {bn} and {cn} are convergentd)if both {bn} and {cn} are convergentCorrect answer is option 'C'. Can you explain this answer?.
Solutions for Let {an}, {bn} and {cn} be sequences of real numbers such that bn = a2n and cn = a2n+1. Then {an} is convergenta)implies {bn} is convergent but {cn} need not be convergentb)implies {cn} is convergent but {bn} need not be convergentc)implies both {bn} and {cn} are convergentd)if both {bn} and {cn} are convergentCorrect answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for Mathematics.
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Let {an}, {bn} and {cn} be sequences of real numbers such that bn = a2n and cn = a2n+1. Then {an} is convergenta)implies {bn} is convergent but {cn} need not be convergentb)implies {cn} is convergent but {bn} need not be convergentc)implies both {bn} and {cn} are convergentd)if both {bn} and {cn} are convergentCorrect answer is option 'C'. Can you explain this answer?, a detailed solution for Let {an}, {bn} and {cn} be sequences of real numbers such that bn = a2n and cn = a2n+1. Then {an} is convergenta)implies {bn} is convergent but {cn} need not be convergentb)implies {cn} is convergent but {bn} need not be convergentc)implies both {bn} and {cn} are convergentd)if both {bn} and {cn} are convergentCorrect answer is option 'C'. Can you explain this answer? has been provided alongside types of Let {an}, {bn} and {cn} be sequences of real numbers such that bn = a2n and cn = a2n+1. Then {an} is convergenta)implies {bn} is convergent but {cn} need not be convergentb)implies {cn} is convergent but {bn} need not be convergentc)implies both {bn} and {cn} are convergentd)if both {bn} and {cn} are convergentCorrect answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice Let {an}, {bn} and {cn} be sequences of real numbers such that bn = a2n and cn = a2n+1. Then {an} is convergenta)implies {bn} is convergent but {cn} need not be convergentb)implies {cn} is convergent but {bn} need not be convergentc)implies both {bn} and {cn} are convergentd)if both {bn} and {cn} are convergentCorrect answer is option 'C'. Can you explain this answer? tests, examples and also practice Mathematics tests.
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