Mixing
Alternating sum of inverse prime numbers [duplicate]
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This question already has an answer here:
Does the alternating sum of prime reciprocals converge?
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It is well known that the sum of all inverse primes is divergent. But the alternating sum is convergent by the Leiniz criterion. To which known constant "a" does the sum converge?
$$a = frac12 - frac13 +frac15-frac17+frac111 -+ ...$$
sequences-and-series prime-numbers
asked Aug 6 at 20:28
Dr. Wolfgang Hintze
2,370515
marked as duplicate by gimusi, Adrian Keister, Xander Henderson, amWhy, max_zorn Aug 7 at 1:08
This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.
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up vote
1
down vote
favorite
This question already has an answer here:
Does the alternating sum of prime reciprocals converge?
3 answers
It is well known that the sum of all inverse primes is divergent. But the alternating sum is convergent by the Leiniz criterion. To which known constant "a" does the sum converge?
$$a = frac12 - frac13 +frac15-frac17+frac111 -+ ...$$
sequences-and-series prime-numbers
asked Aug 6 at 20:28
Dr. Wolfgang Hintze
2,370515
marked as duplicate by gimusi, Adrian Keister, Xander Henderson, amWhy, max_zorn Aug 7 at 1:08
This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.
1
your wording implies that the answer is known, if not to you, then someone. My guess would be that nobody knows.
– Will Jagy
Aug 6 at 20:32
1
You will see an answer here : math.stackexchange.com/questions/241728/…
– Pjonin
Aug 6 at 20:33
@gimusi I have looked at the proposed answer. It deals with the convergence only, which, as I said in my post is granted by the Leibniz criterion. My question asks if the limit is a known constant, or can be expressed by known constants.
– Dr. Wolfgang Hintze
Aug 6 at 20:42
oeis.org/A078437 Only the first few digits are known. All currently known digits: $0.26960635197167dots$
– JMoravitz
Aug 6 at 20:43
@Dr.WolfgangHintze Look at the third answer math.stackexchange.com/a/2329044/505767
– gimusi
Aug 6 at 20:43
 |Â
show 1 more comment
up vote
1
down vote
favorite
up vote
1
down vote
favorite
This question already has an answer here:
Does the alternating sum of prime reciprocals converge?
3 answers
It is well known that the sum of all inverse primes is divergent. But the alternating sum is convergent by the Leiniz criterion. To which known constant "a" does the sum converge?
$$a = frac12 - frac13 +frac15-frac17+frac111 -+ ...$$
sequences-and-series prime-numbers
asked Aug 6 at 20:28
Dr. Wolfgang Hintze
2,370515
This question already has an answer here:
Does the alternating sum of prime reciprocals converge?
3 answers
It is well known that the sum of all inverse primes is divergent. But the alternating sum is convergent by the Leiniz criterion. To which known constant "a" does the sum converge?
$$a = frac12 - frac13 +frac15-frac17+frac111 -+ ...$$
This question already has an answer here:
Does the alternating sum of prime reciprocals converge?
3 answers
sequences-and-series prime-numbers
asked Aug 6 at 20:28
Dr. Wolfgang Hintze
2,370515
edited Aug 6 at 20:31
asked Aug 6 at 20:28
Dr. Wolfgang Hintze
2,370515
asked Aug 6 at 20:28
Dr. Wolfgang Hintze
2,370515
asked Aug 6 at 20:28
Dr. Wolfgang Hintze
2,370515
2,370515
marked as duplicate by gimusi, Adrian Keister, Xander Henderson, amWhy, max_zorn Aug 7 at 1:08
This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.
marked as duplicate by gimusi, Adrian Keister, Xander Henderson, amWhy, max_zorn Aug 7 at 1:08
This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.
1
your wording implies that the answer is known, if not to you, then someone. My guess would be that nobody knows.
– Will Jagy
Aug 6 at 20:32
1
You will see an answer here : math.stackexchange.com/questions/241728/…
– Pjonin
Aug 6 at 20:33
@gimusi I have looked at the proposed answer. It deals with the convergence only, which, as I said in my post is granted by the Leibniz criterion. My question asks if the limit is a known constant, or can be expressed by known constants.
– Dr. Wolfgang Hintze
Aug 6 at 20:42
oeis.org/A078437 Only the first few digits are known. All currently known digits: $0.26960635197167dots$
– JMoravitz
Aug 6 at 20:43
@Dr.WolfgangHintze Look at the third answer math.stackexchange.com/a/2329044/505767
– gimusi
Aug 6 at 20:43
 |Â
show 1 more comment
1
your wording implies that the answer is known, if not to you, then someone. My guess would be that nobody knows.
– Will Jagy
Aug 6 at 20:32
1
You will see an answer here : math.stackexchange.com/questions/241728/…
– Pjonin
Aug 6 at 20:33
@gimusi I have looked at the proposed answer. It deals with the convergence only, which, as I said in my post is granted by the Leibniz criterion. My question asks if the limit is a known constant, or can be expressed by known constants.
– Dr. Wolfgang Hintze
Aug 6 at 20:42
oeis.org/A078437 Only the first few digits are known. All currently known digits: $0.26960635197167dots$
– JMoravitz
Aug 6 at 20:43
@Dr.WolfgangHintze Look at the third answer math.stackexchange.com/a/2329044/505767
– gimusi
Aug 6 at 20:43
1
1
your wording implies that the answer is known, if not to you, then someone. My guess would be that nobody knows.
– Will Jagy
Aug 6 at 20:32
your wording implies that the answer is known, if not to you, then someone. My guess would be that nobody knows.
– Will Jagy
Aug 6 at 20:32
1
1
You will see an answer here : math.stackexchange.com/questions/241728/…
– Pjonin
Aug 6 at 20:33
You will see an answer here : math.stackexchange.com/questions/241728/…
– Pjonin
Aug 6 at 20:33
@gimusi I have looked at the proposed answer. It deals with the convergence only, which, as I said in my post is granted by the Leibniz criterion. My question asks if the limit is a known constant, or can be expressed by known constants.
– Dr. Wolfgang Hintze
Aug 6 at 20:42
@gimusi I have looked at the proposed answer. It deals with the convergence only, which, as I said in my post is granted by the Leibniz criterion. My question asks if the limit is a known constant, or can be expressed by known constants.
– Dr. Wolfgang Hintze
Aug 6 at 20:42
oeis.org/A078437 Only the first few digits are known. All currently known digits: $0.26960635197167dots$
– JMoravitz
Aug 6 at 20:43
oeis.org/A078437 Only the first few digits are known. All currently known digits: $0.26960635197167dots$
– JMoravitz
Aug 6 at 20:43
@Dr.WolfgangHintze Look at the third answer math.stackexchange.com/a/2329044/505767
– gimusi
Aug 6 at 20:43
@Dr.WolfgangHintze Look at the third answer math.stackexchange.com/a/2329044/505767
– gimusi
Aug 6 at 20:43
 |Â
show 1 more comment
1 Answer
1
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1
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For clarity and completeness, I have put the information in the comments into an answer...
As mentioned, this series has an expansion given by the OEIS, which states that the most accurate known estimate of the limit is 0.26960635197167...
The references given therein, as well as others such as Mathworld, Wells, Robinson & Potter and Weisstein indicate that no known closed form of this limit is known, nor does it have its own special name or symbol.
answered Aug 6 at 23:28
Martin Roberts
1,189318
Thank you for your clarifying contribution. This answers my question in the sense that the result of the sum has no name. The duplicate announcement is wrong, however, since the provided link does NOT give an answer to my question. I have explained this clearly in a comment, and I refrain from repeating myself.
– Dr. Wolfgang Hintze
Aug 7 at 15:13
add a comment |Â
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
1
down vote
For clarity and completeness, I have put the information in the comments into an answer...
As mentioned, this series has an expansion given by the OEIS, which states that the most accurate known estimate of the limit is 0.26960635197167...
The references given therein, as well as others such as Mathworld, Wells, Robinson & Potter and Weisstein indicate that no known closed form of this limit is known, nor does it have its own special name or symbol.
answered Aug 6 at 23:28
Martin Roberts
1,189318
Thank you for your clarifying contribution. This answers my question in the sense that the result of the sum has no name. The duplicate announcement is wrong, however, since the provided link does NOT give an answer to my question. I have explained this clearly in a comment, and I refrain from repeating myself.
– Dr. Wolfgang Hintze
Aug 7 at 15:13
add a comment |Â
up vote
1
down vote
For clarity and completeness, I have put the information in the comments into an answer...
As mentioned, this series has an expansion given by the OEIS, which states that the most accurate known estimate of the limit is 0.26960635197167...
The references given therein, as well as others such as Mathworld, Wells, Robinson & Potter and Weisstein indicate that no known closed form of this limit is known, nor does it have its own special name or symbol.
answered Aug 6 at 23:28
Martin Roberts
1,189318
Thank you for your clarifying contribution. This answers my question in the sense that the result of the sum has no name. The duplicate announcement is wrong, however, since the provided link does NOT give an answer to my question. I have explained this clearly in a comment, and I refrain from repeating myself.
– Dr. Wolfgang Hintze
Aug 7 at 15:13
add a comment |Â
up vote
1
down vote
up vote
1
down vote
For clarity and completeness, I have put the information in the comments into an answer...
As mentioned, this series has an expansion given by the OEIS, which states that the most accurate known estimate of the limit is 0.26960635197167...
The references given therein, as well as others such as Mathworld, Wells, Robinson & Potter and Weisstein indicate that no known closed form of this limit is known, nor does it have its own special name or symbol.
answered Aug 6 at 23:28
Martin Roberts
1,189318
For clarity and completeness, I have put the information in the comments into an answer...
As mentioned, this series has an expansion given by the OEIS, which states that the most accurate known estimate of the limit is 0.26960635197167...
The references given therein, as well as others such as Mathworld, Wells, Robinson & Potter and Weisstein indicate that no known closed form of this limit is known, nor does it have its own special name or symbol.
answered Aug 6 at 23:28
Martin Roberts
1,189318
edited Aug 6 at 23:35
answered Aug 6 at 23:28
Martin Roberts
1,189318
answered Aug 6 at 23:28
Martin Roberts
1,189318
answered Aug 6 at 23:28
Martin Roberts
1,189318
1,189318
Thank you for your clarifying contribution. This answers my question in the sense that the result of the sum has no name. The duplicate announcement is wrong, however, since the provided link does NOT give an answer to my question. I have explained this clearly in a comment, and I refrain from repeating myself.
– Dr. Wolfgang Hintze
Aug 7 at 15:13
add a comment |Â
Thank you for your clarifying contribution. This answers my question in the sense that the result of the sum has no name. The duplicate announcement is wrong, however, since the provided link does NOT give an answer to my question. I have explained this clearly in a comment, and I refrain from repeating myself.
– Dr. Wolfgang Hintze
Aug 7 at 15:13
Thank you for your clarifying contribution. This answers my question in the sense that the result of the sum has no name. The duplicate announcement is wrong, however, since the provided link does NOT give an answer to my question. I have explained this clearly in a comment, and I refrain from repeating myself.
– Dr. Wolfgang Hintze
Aug 7 at 15:13
Thank you for your clarifying contribution. This answers my question in the sense that the result of the sum has no name. The duplicate announcement is wrong, however, since the provided link does NOT give an answer to my question. I have explained this clearly in a comment, and I refrain from repeating myself.
– Dr. Wolfgang Hintze
Aug 7 at 15:13
add a comment |Â
1
your wording implies that the answer is known, if not to you, then someone. My guess would be that nobody knows.
– Will Jagy
Aug 6 at 20:32
1
You will see an answer here : math.stackexchange.com/questions/241728/…
– Pjonin
Aug 6 at 20:33
@gimusi I have looked at the proposed answer. It deals with the convergence only, which, as I said in my post is granted by the Leibniz criterion. My question asks if the limit is a known constant, or can be expressed by known constants.
– Dr. Wolfgang Hintze
Aug 6 at 20:42
oeis.org/A078437 Only the first few digits are known. All currently known digits: $0.26960635197167dots$
– JMoravitz
Aug 6 at 20:43
@Dr.WolfgangHintze Look at the third answer math.stackexchange.com/a/2329044/505767
– gimusi
Aug 6 at 20:43