How to show infinite series diverge? [closed]
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Show that the infinite series $sum_{n=1}^{+∞}frac1{2(2n+1)}$ and $sum_{n=1}^{+∞}-frac1{2(2n+3)}$ both diverge.
sequences-and-series divergent-series
edited Dec 3 at 19:27
gimusi
91.4k74495
asked Dec 3 at 19:17
L.Lynch
12
closed as off-topic by Did, Xander Henderson, T. Bongers, quid♦ Dec 4 at 1:07
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Did, Xander Henderson, T. Bongers, quid
If this question can be reworded to fit the rules in the help center, please edit the question.
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up vote
-3
down vote
favorite
Show that the infinite series $sum_{n=1}^{+∞}frac1{2(2n+1)}$ and $sum_{n=1}^{+∞}-frac1{2(2n+3)}$ both diverge.
sequences-and-series divergent-series
edited Dec 3 at 19:27
gimusi
91.4k74495
asked Dec 3 at 19:17
L.Lynch
12
closed as off-topic by Did, Xander Henderson, T. Bongers, quid♦ Dec 4 at 1:07
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Did, Xander Henderson, T. Bongers, quid
If this question can be reworded to fit the rules in the help center, please edit the question.
As written, the $2n+1$ and $2n+3$ are in the numerator, so the terms do not go to zero, so the sums diverge. I presume that you meant them in the denominator. In that case these look a lot like the harmonic series. Do you know the sum of that diverges? Can you use that fact to prove these diverge?
– Ross Millikan
Dec 3 at 19:27
Which methods you know to study the convergence for a series? What about $sum 1/n$?
– gimusi
Dec 3 at 19:49
1
@L.Lynch Welcome to MSE. Please keep in mind that this is not a do-my-homework site, and many users are rather put off by questions that feel like that. As such, if you were to edit your question to include your thoughts and the context where you met this problem, it would receive a far more positive response.
– T. Bongers
Dec 3 at 22:58
add a comment |
up vote
-3
down vote
favorite
up vote
-3
down vote
favorite
Show that the infinite series $sum_{n=1}^{+∞}frac1{2(2n+1)}$ and $sum_{n=1}^{+∞}-frac1{2(2n+3)}$ both diverge.
sequences-and-series divergent-series
edited Dec 3 at 19:27
gimusi
91.4k74495
asked Dec 3 at 19:17
L.Lynch
12
Show that the infinite series $sum_{n=1}^{+∞}frac1{2(2n+1)}$ and $sum_{n=1}^{+∞}-frac1{2(2n+3)}$ both diverge.
sequences-and-series divergent-series
sequences-and-series divergent-series
edited Dec 3 at 19:27
gimusi
91.4k74495
asked Dec 3 at 19:17
L.Lynch
12
edited Dec 3 at 19:27
gimusi
91.4k74495
asked Dec 3 at 19:17
L.Lynch
12
edited Dec 3 at 19:27
gimusi
91.4k74495
edited Dec 3 at 19:27
gimusi
91.4k74495
edited Dec 3 at 19:27
gimusi
91.4k74495
91.4k74495
asked Dec 3 at 19:17
L.Lynch
12
asked Dec 3 at 19:17
L.Lynch
12
asked Dec 3 at 19:17
L.Lynch
12
12
closed as off-topic by Did, Xander Henderson, T. Bongers, quid♦ Dec 4 at 1:07
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Did, Xander Henderson, T. Bongers, quid
If this question can be reworded to fit the rules in the help center, please edit the question.
closed as off-topic by Did, Xander Henderson, T. Bongers, quid♦ Dec 4 at 1:07
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Did, Xander Henderson, T. Bongers, quid
If this question can be reworded to fit the rules in the help center, please edit the question.
As written, the $2n+1$ and $2n+3$ are in the numerator, so the terms do not go to zero, so the sums diverge. I presume that you meant them in the denominator. In that case these look a lot like the harmonic series. Do you know the sum of that diverges? Can you use that fact to prove these diverge?
– Ross Millikan
Dec 3 at 19:27
Which methods you know to study the convergence for a series? What about $sum 1/n$?
– gimusi
Dec 3 at 19:49
1
@L.Lynch Welcome to MSE. Please keep in mind that this is not a do-my-homework site, and many users are rather put off by questions that feel like that. As such, if you were to edit your question to include your thoughts and the context where you met this problem, it would receive a far more positive response.
– T. Bongers
Dec 3 at 22:58
add a comment |
As written, the $2n+1$ and $2n+3$ are in the numerator, so the terms do not go to zero, so the sums diverge. I presume that you meant them in the denominator. In that case these look a lot like the harmonic series. Do you know the sum of that diverges? Can you use that fact to prove these diverge?
– Ross Millikan
Dec 3 at 19:27
Which methods you know to study the convergence for a series? What about $sum 1/n$?
– gimusi
Dec 3 at 19:49
1
@L.Lynch Welcome to MSE. Please keep in mind that this is not a do-my-homework site, and many users are rather put off by questions that feel like that. As such, if you were to edit your question to include your thoughts and the context where you met this problem, it would receive a far more positive response.
– T. Bongers
Dec 3 at 22:58
As written, the $2n+1$ and $2n+3$ are in the numerator, so the terms do not go to zero, so the sums diverge. I presume that you meant them in the denominator. In that case these look a lot like the harmonic series. Do you know the sum of that diverges? Can you use that fact to prove these diverge?
– Ross Millikan
Dec 3 at 19:27
As written, the $2n+1$ and $2n+3$ are in the numerator, so the terms do not go to zero, so the sums diverge. I presume that you meant them in the denominator. In that case these look a lot like the harmonic series. Do you know the sum of that diverges? Can you use that fact to prove these diverge?
– Ross Millikan
Dec 3 at 19:27
Which methods you know to study the convergence for a series? What about $sum 1/n$?
– gimusi
Dec 3 at 19:49
Which methods you know to study the convergence for a series? What about $sum 1/n$?
– gimusi
Dec 3 at 19:49
1
1
@L.Lynch Welcome to MSE. Please keep in mind that this is not a do-my-homework site, and many users are rather put off by questions that feel like that. As such, if you were to edit your question to include your thoughts and the context where you met this problem, it would receive a far more positive response.
– T. Bongers
Dec 3 at 22:58
@L.Lynch Welcome to MSE. Please keep in mind that this is not a do-my-homework site, and many users are rather put off by questions that feel like that. As such, if you were to edit your question to include your thoughts and the context where you met this problem, it would receive a far more positive response.
– T. Bongers
Dec 3 at 22:58
add a comment |
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As written, the $2n+1$ and $2n+3$ are in the numerator, so the terms do not go to zero, so the sums diverge. I presume that you meant them in the denominator. In that case these look a lot like the harmonic series. Do you know the sum of that diverges? Can you use that fact to prove these diverge?
– Ross Millikan
Dec 3 at 19:27
Which methods you know to study the convergence for a series? What about $sum 1/n$?
– gimusi
Dec 3 at 19:49
1
@L.Lynch Welcome to MSE. Please keep in mind that this is not a do-my-homework site, and many users are rather put off by questions that feel like that. As such, if you were to edit your question to include your thoughts and the context where you met this problem, it would receive a far more positive response.
– T. Bongers
Dec 3 at 22:58