Mixing
Types of sequences
Clash Royale CLAN TAG#URR8PPP
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I was given this question. It asked to state which of the sequences, $a_n$, $b_n$ and $u_n$ are divergent, convergent or periodic.
The given info is:
$$u_1 = 1 \
u_ncdot u_n+1 =2\
a_n = u_n+1 + u_n\
b_n = u_n+1 - u_n$$
I got $u_n$ to be $1,2,1,2,dots$
$a_n$ to be $3,3,3,3,3,dots$
$b_n$ to be $1,-1,1,-1,1,dots$
So granted that I worked these out correctly. I'm guessing $u_n$ and $b_n$ are periodic, however I'm not sure about $a_n$.
sequences-and-series convergence
asked Aug 3 at 1:39
user122343
445
 |Â
show 5 more comments
up vote
1
down vote
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I was given this question. It asked to state which of the sequences, $a_n$, $b_n$ and $u_n$ are divergent, convergent or periodic.
The given info is:
$$u_1 = 1 \
u_ncdot u_n+1 =2\
a_n = u_n+1 + u_n\
b_n = u_n+1 - u_n$$
I got $u_n$ to be $1,2,1,2,dots$
$a_n$ to be $3,3,3,3,3,dots$
$b_n$ to be $1,-1,1,-1,1,dots$
So granted that I worked these out correctly. I'm guessing $u_n$ and $b_n$ are periodic, however I'm not sure about $a_n$.
sequences-and-series convergence
asked Aug 3 at 1:39
user122343
445
Please take the time to format your question and equations properly using MathJax and $LaTeX$. It is quite unclear what you are after at the moment.
– JMoravitz
Aug 3 at 1:42
Take a bit more time in deciding which tags to tag your question with. The tag (self-learning) for example should only be used for questions about pedagogy and the actual action of learning on your own (E.g. how frequently should I give myself homework and practice mock exams if I'm teaching myself such and such topic). It should never be used on a question which is about the content of what it is you are studying rather than a question about the process of studying. Similarly, (proof-theory) is an irrelevant tag here as well.
– JMoravitz
Aug 3 at 1:45
Yes, your conclusions look correct for $U_n$ and $a_n$. However, $b_1=U_2-U_1=2-1=1$, $b_2=U_3-U_2=1-2=-1$, $b_4=U_5-U_4=1-2=1$,... The classification would label $U_n$ periodic, $a_n$ periodic and convergent, and $b_n$ periodic and divergent.
– spiralstotheleft
Aug 3 at 1:49
1
@spiralstotheleft okay thanks. So I'm guessing $a_n$ converges to 3 ? Also I don't get how $b_n$ is divergent
– user122343
Aug 3 at 1:53
Please check that I have typeset the equations correctly. As for the content of the question, every sequence which is not convergent is said to be divergent, but the types of divergence can be classified further. Assuming your work is correct, $a_n$ would appear to be a constant sequence which is an example of a convergent sequence. Both $b_n$ and $u_n$ appear to be divergent periodic sequences. These should be proven if you want to be certain. Induction would be a good tool to use here.
– JMoravitz
Aug 3 at 1:54
 |Â
show 5 more comments
up vote
1
down vote
favorite
up vote
1
down vote
favorite
I was given this question. It asked to state which of the sequences, $a_n$, $b_n$ and $u_n$ are divergent, convergent or periodic.
The given info is:
$$u_1 = 1 \
u_ncdot u_n+1 =2\
a_n = u_n+1 + u_n\
b_n = u_n+1 - u_n$$
I got $u_n$ to be $1,2,1,2,dots$
$a_n$ to be $3,3,3,3,3,dots$
$b_n$ to be $1,-1,1,-1,1,dots$
So granted that I worked these out correctly. I'm guessing $u_n$ and $b_n$ are periodic, however I'm not sure about $a_n$.
sequences-and-series convergence
asked Aug 3 at 1:39
user122343
445
I was given this question. It asked to state which of the sequences, $a_n$, $b_n$ and $u_n$ are divergent, convergent or periodic.
The given info is:
$$u_1 = 1 \
u_ncdot u_n+1 =2\
a_n = u_n+1 + u_n\
b_n = u_n+1 - u_n$$
I got $u_n$ to be $1,2,1,2,dots$
$a_n$ to be $3,3,3,3,3,dots$
$b_n$ to be $1,-1,1,-1,1,dots$
So granted that I worked these out correctly. I'm guessing $u_n$ and $b_n$ are periodic, however I'm not sure about $a_n$.
sequences-and-series convergence
asked Aug 3 at 1:39
user122343
445
edited Aug 3 at 2:01
asked Aug 3 at 1:39
user122343
445
asked Aug 3 at 1:39
user122343
445
asked Aug 3 at 1:39
user122343
445
445
Please take the time to format your question and equations properly using MathJax and $LaTeX$. It is quite unclear what you are after at the moment.
– JMoravitz
Aug 3 at 1:42
Take a bit more time in deciding which tags to tag your question with. The tag (self-learning) for example should only be used for questions about pedagogy and the actual action of learning on your own (E.g. how frequently should I give myself homework and practice mock exams if I'm teaching myself such and such topic). It should never be used on a question which is about the content of what it is you are studying rather than a question about the process of studying. Similarly, (proof-theory) is an irrelevant tag here as well.
– JMoravitz
Aug 3 at 1:45
Yes, your conclusions look correct for $U_n$ and $a_n$. However, $b_1=U_2-U_1=2-1=1$, $b_2=U_3-U_2=1-2=-1$, $b_4=U_5-U_4=1-2=1$,... The classification would label $U_n$ periodic, $a_n$ periodic and convergent, and $b_n$ periodic and divergent.
– spiralstotheleft
Aug 3 at 1:49
1
@spiralstotheleft okay thanks. So I'm guessing $a_n$ converges to 3 ? Also I don't get how $b_n$ is divergent
– user122343
Aug 3 at 1:53
Please check that I have typeset the equations correctly. As for the content of the question, every sequence which is not convergent is said to be divergent, but the types of divergence can be classified further. Assuming your work is correct, $a_n$ would appear to be a constant sequence which is an example of a convergent sequence. Both $b_n$ and $u_n$ appear to be divergent periodic sequences. These should be proven if you want to be certain. Induction would be a good tool to use here.
– JMoravitz
Aug 3 at 1:54
 |Â
show 5 more comments
Please take the time to format your question and equations properly using MathJax and $LaTeX$. It is quite unclear what you are after at the moment.
– JMoravitz
Aug 3 at 1:42
Take a bit more time in deciding which tags to tag your question with. The tag (self-learning) for example should only be used for questions about pedagogy and the actual action of learning on your own (E.g. how frequently should I give myself homework and practice mock exams if I'm teaching myself such and such topic). It should never be used on a question which is about the content of what it is you are studying rather than a question about the process of studying. Similarly, (proof-theory) is an irrelevant tag here as well.
– JMoravitz
Aug 3 at 1:45
Yes, your conclusions look correct for $U_n$ and $a_n$. However, $b_1=U_2-U_1=2-1=1$, $b_2=U_3-U_2=1-2=-1$, $b_4=U_5-U_4=1-2=1$,... The classification would label $U_n$ periodic, $a_n$ periodic and convergent, and $b_n$ periodic and divergent.
– spiralstotheleft
Aug 3 at 1:49
1
@spiralstotheleft okay thanks. So I'm guessing $a_n$ converges to 3 ? Also I don't get how $b_n$ is divergent
– user122343
Aug 3 at 1:53
Please check that I have typeset the equations correctly. As for the content of the question, every sequence which is not convergent is said to be divergent, but the types of divergence can be classified further. Assuming your work is correct, $a_n$ would appear to be a constant sequence which is an example of a convergent sequence. Both $b_n$ and $u_n$ appear to be divergent periodic sequences. These should be proven if you want to be certain. Induction would be a good tool to use here.
– JMoravitz
Aug 3 at 1:54
Please take the time to format your question and equations properly using MathJax and $LaTeX$. It is quite unclear what you are after at the moment.
– JMoravitz
Aug 3 at 1:42
Please take the time to format your question and equations properly using MathJax and $LaTeX$. It is quite unclear what you are after at the moment.
– JMoravitz
Aug 3 at 1:42
Take a bit more time in deciding which tags to tag your question with. The tag (self-learning) for example should only be used for questions about pedagogy and the actual action of learning on your own (E.g. how frequently should I give myself homework and practice mock exams if I'm teaching myself such and such topic). It should never be used on a question which is about the content of what it is you are studying rather than a question about the process of studying. Similarly, (proof-theory) is an irrelevant tag here as well.
– JMoravitz
Aug 3 at 1:45
Take a bit more time in deciding which tags to tag your question with. The tag (self-learning) for example should only be used for questions about pedagogy and the actual action of learning on your own (E.g. how frequently should I give myself homework and practice mock exams if I'm teaching myself such and such topic). It should never be used on a question which is about the content of what it is you are studying rather than a question about the process of studying. Similarly, (proof-theory) is an irrelevant tag here as well.
– JMoravitz
Aug 3 at 1:45
Yes, your conclusions look correct for $U_n$ and $a_n$. However, $b_1=U_2-U_1=2-1=1$, $b_2=U_3-U_2=1-2=-1$, $b_4=U_5-U_4=1-2=1$,... The classification would label $U_n$ periodic, $a_n$ periodic and convergent, and $b_n$ periodic and divergent.
– spiralstotheleft
Aug 3 at 1:49
Yes, your conclusions look correct for $U_n$ and $a_n$. However, $b_1=U_2-U_1=2-1=1$, $b_2=U_3-U_2=1-2=-1$, $b_4=U_5-U_4=1-2=1$,... The classification would label $U_n$ periodic, $a_n$ periodic and convergent, and $b_n$ periodic and divergent.
– spiralstotheleft
Aug 3 at 1:49
1
1
@spiralstotheleft okay thanks. So I'm guessing $a_n$ converges to 3 ? Also I don't get how $b_n$ is divergent
– user122343
Aug 3 at 1:53
@spiralstotheleft okay thanks. So I'm guessing $a_n$ converges to 3 ? Also I don't get how $b_n$ is divergent
– user122343
Aug 3 at 1:53
Please check that I have typeset the equations correctly. As for the content of the question, every sequence which is not convergent is said to be divergent, but the types of divergence can be classified further. Assuming your work is correct, $a_n$ would appear to be a constant sequence which is an example of a convergent sequence. Both $b_n$ and $u_n$ appear to be divergent periodic sequences. These should be proven if you want to be certain. Induction would be a good tool to use here.
– JMoravitz
Aug 3 at 1:54
Please check that I have typeset the equations correctly. As for the content of the question, every sequence which is not convergent is said to be divergent, but the types of divergence can be classified further. Assuming your work is correct, $a_n$ would appear to be a constant sequence which is an example of a convergent sequence. Both $b_n$ and $u_n$ appear to be divergent periodic sequences. These should be proven if you want to be certain. Induction would be a good tool to use here.
– JMoravitz
Aug 3 at 1:54
 |Â
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Please take the time to format your question and equations properly using MathJax and $LaTeX$. It is quite unclear what you are after at the moment.
– JMoravitz
Aug 3 at 1:42
Take a bit more time in deciding which tags to tag your question with. The tag (self-learning) for example should only be used for questions about pedagogy and the actual action of learning on your own (E.g. how frequently should I give myself homework and practice mock exams if I'm teaching myself such and such topic). It should never be used on a question which is about the content of what it is you are studying rather than a question about the process of studying. Similarly, (proof-theory) is an irrelevant tag here as well.
– JMoravitz
Aug 3 at 1:45
Yes, your conclusions look correct for $U_n$ and $a_n$. However, $b_1=U_2-U_1=2-1=1$, $b_2=U_3-U_2=1-2=-1$, $b_4=U_5-U_4=1-2=1$,... The classification would label $U_n$ periodic, $a_n$ periodic and convergent, and $b_n$ periodic and divergent.
– spiralstotheleft
Aug 3 at 1:49
1
@spiralstotheleft okay thanks. So I'm guessing $a_n$ converges to 3 ? Also I don't get how $b_n$ is divergent
– user122343
Aug 3 at 1:53
Please check that I have typeset the equations correctly. As for the content of the question, every sequence which is not convergent is said to be divergent, but the types of divergence can be classified further. Assuming your work is correct, $a_n$ would appear to be a constant sequence which is an example of a convergent sequence. Both $b_n$ and $u_n$ appear to be divergent periodic sequences. These should be proven if you want to be certain. Induction would be a good tool to use here.
– JMoravitz
Aug 3 at 1:54