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Can a bounded and a NON monotonic succession converge?
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Being $a_n_nin N $ a succession of real numbers which is bounded and NOT monotonic, can the succesion converge?
To answer the question I must find one succesion $a_n$ that converges, For example:
$$a_n = (-1)^nleft(frac1nright)$$
Which converges, is bounded and is not monotonic (as far as I know) then the answer to the question is YES?
real-analysis limits proof-verification
edited 2 hours ago
José Carlos Santos
131k17106192
asked 2 hours ago
Martin B.S.
477
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Martin B.S. is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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up vote
2
down vote
favorite
Being $a_n_nin N $ a succession of real numbers which is bounded and NOT monotonic, can the succesion converge?
To answer the question I must find one succesion $a_n$ that converges, For example:
$$a_n = (-1)^nleft(frac1nright)$$
Which converges, is bounded and is not monotonic (as far as I know) then the answer to the question is YES?
real-analysis limits proof-verification
edited 2 hours ago
José Carlos Santos
131k17106192
asked 2 hours ago
Martin B.S.
477
New contributor
Martin B.S. is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
The question is if the succesion CAN converge, not that every succession which is bounded and is not monotonic will converge. $(-1)^n$ surely doesnt converge and is bounded and not monotonic.
– Martin B.S.
2 hours ago
add a comment |Â
up vote
2
down vote
favorite
up vote
2
down vote
favorite
Being $a_n_nin N $ a succession of real numbers which is bounded and NOT monotonic, can the succesion converge?
To answer the question I must find one succesion $a_n$ that converges, For example:
$$a_n = (-1)^nleft(frac1nright)$$
Which converges, is bounded and is not monotonic (as far as I know) then the answer to the question is YES?
real-analysis limits proof-verification
edited 2 hours ago
José Carlos Santos
131k17106192
asked 2 hours ago
Martin B.S.
477
New contributor
Martin B.S. is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Being $a_n_nin N $ a succession of real numbers which is bounded and NOT monotonic, can the succesion converge?
To answer the question I must find one succesion $a_n$ that converges, For example:
$$a_n = (-1)^nleft(frac1nright)$$
Which converges, is bounded and is not monotonic (as far as I know) then the answer to the question is YES?
real-analysis limits proof-verification
real-analysis limits proof-verification
edited 2 hours ago
José Carlos Santos
131k17106192
asked 2 hours ago
Martin B.S.
477
New contributor
Martin B.S. is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
edited 2 hours ago
José Carlos Santos
131k17106192
asked 2 hours ago
Martin B.S.
477
New contributor
Martin B.S. is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
edited 2 hours ago
José Carlos Santos
131k17106192
edited 2 hours ago
José Carlos Santos
131k17106192
edited 2 hours ago
José Carlos Santos
131k17106192
131k17106192
asked 2 hours ago
Martin B.S.
477
New contributor
Martin B.S. is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 2 hours ago
Martin B.S.
477
asked 2 hours ago
Martin B.S.
477
477
New contributor
Martin B.S. is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
Martin B.S. is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Martin B.S. is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
The question is if the succesion CAN converge, not that every succession which is bounded and is not monotonic will converge. $(-1)^n$ surely doesnt converge and is bounded and not monotonic.
– Martin B.S.
2 hours ago
add a comment |Â
The question is if the succesion CAN converge, not that every succession which is bounded and is not monotonic will converge. $(-1)^n$ surely doesnt converge and is bounded and not monotonic.
– Martin B.S.
2 hours ago
The question is if the succesion CAN converge, not that every succession which is bounded and is not monotonic will converge. $(-1)^n$ surely doesnt converge and is bounded and not monotonic.
– Martin B.S.
2 hours ago
The question is if the succesion CAN converge, not that every succession which is bounded and is not monotonic will converge. $(-1)^n$ surely doesnt converge and is bounded and not monotonic.
– Martin B.S.
2 hours ago
add a comment |Â
1 Answer
1
active
oldest
votes
up vote
3
down vote
accepted
Yes. Since the question is whether a certain thing can happen and since you found a situation in which that thing does happen, the answer is affirmative.
answered 2 hours ago
José Carlos Santos
131k17106192
add a comment |Â
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
3
down vote
accepted
Yes. Since the question is whether a certain thing can happen and since you found a situation in which that thing does happen, the answer is affirmative.
answered 2 hours ago
José Carlos Santos
131k17106192
add a comment |Â
up vote
3
down vote
accepted
Yes. Since the question is whether a certain thing can happen and since you found a situation in which that thing does happen, the answer is affirmative.
answered 2 hours ago
José Carlos Santos
131k17106192
add a comment |Â
up vote
3
down vote
accepted
up vote
3
down vote
accepted
Yes. Since the question is whether a certain thing can happen and since you found a situation in which that thing does happen, the answer is affirmative.
answered 2 hours ago
José Carlos Santos
131k17106192
Yes. Since the question is whether a certain thing can happen and since you found a situation in which that thing does happen, the answer is affirmative.
answered 2 hours ago
José Carlos Santos
131k17106192
answered 2 hours ago
José Carlos Santos
131k17106192
answered 2 hours ago
José Carlos Santos
131k17106192
answered 2 hours ago
José Carlos Santos
131k17106192
131k17106192
add a comment |Â
add a comment |Â
Martin B.S. is a new contributor. Be nice, and check out our Code of Conduct.
Martin B.S. is a new contributor. Be nice, and check out our Code of Conduct.
Martin B.S. is a new contributor. Be nice, and check out our Code of Conduct.
Martin B.S. is a new contributor. Be nice, and check out our Code of Conduct.
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The question is if the succesion CAN converge, not that every succession which is bounded and is not monotonic will converge. $(-1)^n$ surely doesnt converge and is bounded and not monotonic.
– Martin B.S.
2 hours ago