Mathematics Exam > Mathematics Questions > Let {an} = {1,11/2,1/3, \ 1/2,1/3,1/4,1,1/2,1...
Start Learning for Free
Let {an} = {1,11/2,1/3, \ 1/2,1/3,1/4,1,1/2,1/3,1/4,1/5....} be a sequence of real numbers, then
- a){an} has infinite number of limit points
- b){an} has infinite number of convergent subsequence,
- c)
- d)
Correct answer is option 'A,B,C,D'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
Let {an} = {1,11/2,1/3, \ 1/2,1/3,1/4,1,1/2,1/3,1/4,1/5....}be a seque...
We know
and
Now here it is clear that every point of given sequence be its limit point and clearly sequence has infinitely many terms.
⇒ Given sequence has infinite number of limit points.
Now by theorem we know if sequence has a limit point then
a convergent subsequence which converge to that limit point.
Since sequence has infinite number of limit points.
⇒ Corresponding to each limit points, there is subspace which converge to that limit point.
⇒ There are infinite number of convergent subsequences of sequence {an}
and
Now here it is clear that every point of given sequence be its limit point and clearly sequence has infinitely many terms.
⇒ Given sequence has infinite number of limit points.
Now by theorem we know if sequence has a limit point then
a convergent subsequence which converge to that limit point.Since sequence has infinite number of limit points.
⇒ Corresponding to each limit points, there is subspace which converge to that limit point.
⇒ There are infinite number of convergent subsequences of sequence {an}
Most Upvoted Answer
Let {an} = {1,11/2,1/3, \ 1/2,1/3,1/4,1,1/2,1/3,1/4,1/5....}be a seque...
We know
and
Now here it is clear that every point of given sequence be its limit point and clearly sequence has infinitely many terms.
⇒ Given sequence has infinite number of limit points.
Now by theorem we know if sequence has a limit point then
a convergent subsequence which converge to that limit point.
Since sequence has infinite number of limit points.
⇒ Corresponding to each limit points, there is subspace which converge to that limit point.
⇒ There are infinite number of convergent subsequences of sequence {an}
and
Now here it is clear that every point of given sequence be its limit point and clearly sequence has infinitely many terms.
⇒ Given sequence has infinite number of limit points.
Now by theorem we know if sequence has a limit point then
a convergent subsequence which converge to that limit point.Since sequence has infinite number of limit points.
⇒ Corresponding to each limit points, there is subspace which converge to that limit point.
⇒ There are infinite number of convergent subsequences of sequence {an}
Free Test
FREE
| Start Free Test |
Community Answer
Let {an} = {1,11/2,1/3, \ 1/2,1/3,1/4,1,1/2,1/3,1/4,1/5....}be a seque...
We know
and
Now here it is clear that every point of given sequence be its limit point and clearly sequence has infinitely many terms.
⇒ Given sequence has infinite number of limit points.
Now by theorem we know if sequence has a limit point then a convergent subsequence which converge to that limit point.
Since sequence has infinite number of limit points.
⇒ Corresponding to each limit points, there is subspace which converge to that limit point.
⇒ There are infinite number of convergent subsequences of sequence {an}
and
Now here it is clear that every point of given sequence be its limit point and clearly sequence has infinitely many terms.
⇒ Given sequence has infinite number of limit points.
Now by theorem we know if sequence has a limit point then
a convergent subsequence which converge to that limit point.Since sequence has infinite number of limit points.
⇒ Corresponding to each limit points, there is subspace which converge to that limit point.
⇒ There are infinite number of convergent subsequences of sequence {an}
|
Explore Courses for Mathematics exam
|
|
Similar Mathematics Doubts
Let {an} = {1,11/2,1/3, \ 1/2,1/3,1/4,1,1/2,1/3,1/4,1/5....}be a sequence ofreal numbers, thena){an} has infinite number of limit pointsb){an} has infinite number of convergent subsequence,c)d)Correct answer is option 'A,B,C,D'. Can you explain this answer?
Question Description
Let {an} = {1,11/2,1/3, \ 1/2,1/3,1/4,1,1/2,1/3,1/4,1/5....}be a sequence ofreal numbers, thena){an} has infinite number of limit pointsb){an} has infinite number of convergent subsequence,c)d)Correct answer is option 'A,B,C,D'. 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} = {1,11/2,1/3, \ 1/2,1/3,1/4,1,1/2,1/3,1/4,1/5....}be a sequence ofreal numbers, thena){an} has infinite number of limit pointsb){an} has infinite number of convergent subsequence,c)d)Correct answer is option 'A,B,C,D'. 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} = {1,11/2,1/3, \ 1/2,1/3,1/4,1,1/2,1/3,1/4,1/5....}be a sequence ofreal numbers, thena){an} has infinite number of limit pointsb){an} has infinite number of convergent subsequence,c)d)Correct answer is option 'A,B,C,D'. Can you explain this answer?.
Let {an} = {1,11/2,1/3, \ 1/2,1/3,1/4,1,1/2,1/3,1/4,1/5....}be a sequence ofreal numbers, thena){an} has infinite number of limit pointsb){an} has infinite number of convergent subsequence,c)d)Correct answer is option 'A,B,C,D'. 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} = {1,11/2,1/3, \ 1/2,1/3,1/4,1,1/2,1/3,1/4,1/5....}be a sequence ofreal numbers, thena){an} has infinite number of limit pointsb){an} has infinite number of convergent subsequence,c)d)Correct answer is option 'A,B,C,D'. 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} = {1,11/2,1/3, \ 1/2,1/3,1/4,1,1/2,1/3,1/4,1/5....}be a sequence ofreal numbers, thena){an} has infinite number of limit pointsb){an} has infinite number of convergent subsequence,c)d)Correct answer is option 'A,B,C,D'. Can you explain this answer?.
Solutions for Let {an} = {1,11/2,1/3, \ 1/2,1/3,1/4,1,1/2,1/3,1/4,1/5....}be a sequence ofreal numbers, thena){an} has infinite number of limit pointsb){an} has infinite number of convergent subsequence,c)d)Correct answer is option 'A,B,C,D'. Can you explain this answer? in English & in Hindi are available as part of our courses for Mathematics.
Download more important topics, notes, lectures and mock test series for Mathematics Exam by signing up for free.
Here you can find the meaning of Let {an} = {1,11/2,1/3, \ 1/2,1/3,1/4,1,1/2,1/3,1/4,1/5....}be a sequence ofreal numbers, thena){an} has infinite number of limit pointsb){an} has infinite number of convergent subsequence,c)d)Correct answer is option 'A,B,C,D'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
Let {an} = {1,11/2,1/3, \ 1/2,1/3,1/4,1,1/2,1/3,1/4,1/5....}be a sequence ofreal numbers, thena){an} has infinite number of limit pointsb){an} has infinite number of convergent subsequence,c)d)Correct answer is option 'A,B,C,D'. Can you explain this answer?, a detailed solution for Let {an} = {1,11/2,1/3, \ 1/2,1/3,1/4,1,1/2,1/3,1/4,1/5....}be a sequence ofreal numbers, thena){an} has infinite number of limit pointsb){an} has infinite number of convergent subsequence,c)d)Correct answer is option 'A,B,C,D'. Can you explain this answer? has been provided alongside types of Let {an} = {1,11/2,1/3, \ 1/2,1/3,1/4,1,1/2,1/3,1/4,1/5....}be a sequence ofreal numbers, thena){an} has infinite number of limit pointsb){an} has infinite number of convergent subsequence,c)d)Correct answer is option 'A,B,C,D'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice Let {an} = {1,11/2,1/3, \ 1/2,1/3,1/4,1,1/2,1/3,1/4,1/5....}be a sequence ofreal numbers, thena){an} has infinite number of limit pointsb){an} has infinite number of convergent subsequence,c)d)Correct answer is option 'A,B,C,D'. Can you explain this answer? tests, examples and also practice Mathematics tests.
|
|
Explore Courses for Mathematics exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup