Prove that$sum_{n=1}^{infty} 2^{-2^{n}}$ converges to an irrational limit. [closed]
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Prove that$sum_{n=1}^{infty} 2^{-2^{n}}$ converges to an irrational limit.
convergence
asked Nov 23 at 22:25
You Zhou
404
closed as off-topic by Scientifica, Ivo Terek, Jean-Claude Arbaut, Brahadeesh, Rebellos Nov 24 at 9:08
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." – Scientifica, Ivo Terek, Jean-Claude Arbaut, Brahadeesh, Rebellos
If this question can be reworded to fit the rules in the help center, please edit the question.
add a comment |
up vote
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Prove that$sum_{n=1}^{infty} 2^{-2^{n}}$ converges to an irrational limit.
convergence
asked Nov 23 at 22:25
You Zhou
404
closed as off-topic by Scientifica, Ivo Terek, Jean-Claude Arbaut, Brahadeesh, Rebellos Nov 24 at 9:08
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." – Scientifica, Ivo Terek, Jean-Claude Arbaut, Brahadeesh, Rebellos
If this question can be reworded to fit the rules in the help center, please edit the question.
What makes you think that?
– user1892304
Nov 23 at 22:30
1
You are asking different thing in the post from the title.
– user587192
Nov 23 at 22:31
Sorry, I fixed it now.
– You Zhou
Nov 23 at 22:38
1
Consider the development of the limit in base $2$. Is it periodic?
– Jean-Claude Arbaut
Nov 23 at 22:39
showing it is even transcendental should not be too hard, given that it has so good approximations
– Hagen von Eitzen
Nov 23 at 22:57
add a comment |
up vote
1
down vote
favorite
up vote
1
down vote
favorite
Prove that$sum_{n=1}^{infty} 2^{-2^{n}}$ converges to an irrational limit.
convergence
asked Nov 23 at 22:25
You Zhou
404
Prove that$sum_{n=1}^{infty} 2^{-2^{n}}$ converges to an irrational limit.
convergence
convergence
asked Nov 23 at 22:25
You Zhou
404
asked Nov 23 at 22:25
You Zhou
404
edited Nov 23 at 22:38
asked Nov 23 at 22:25
You Zhou
404
asked Nov 23 at 22:25
You Zhou
404
asked Nov 23 at 22:25
You Zhou
404
404
closed as off-topic by Scientifica, Ivo Terek, Jean-Claude Arbaut, Brahadeesh, Rebellos Nov 24 at 9:08
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." – Scientifica, Ivo Terek, Jean-Claude Arbaut, Brahadeesh, Rebellos
If this question can be reworded to fit the rules in the help center, please edit the question.
closed as off-topic by Scientifica, Ivo Terek, Jean-Claude Arbaut, Brahadeesh, Rebellos Nov 24 at 9:08
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." – Scientifica, Ivo Terek, Jean-Claude Arbaut, Brahadeesh, Rebellos
If this question can be reworded to fit the rules in the help center, please edit the question.
What makes you think that?
– user1892304
Nov 23 at 22:30
1
You are asking different thing in the post from the title.
– user587192
Nov 23 at 22:31
Sorry, I fixed it now.
– You Zhou
Nov 23 at 22:38
1
Consider the development of the limit in base $2$. Is it periodic?
– Jean-Claude Arbaut
Nov 23 at 22:39
showing it is even transcendental should not be too hard, given that it has so good approximations
– Hagen von Eitzen
Nov 23 at 22:57
add a comment |
What makes you think that?
– user1892304
Nov 23 at 22:30
1
You are asking different thing in the post from the title.
– user587192
Nov 23 at 22:31
Sorry, I fixed it now.
– You Zhou
Nov 23 at 22:38
1
Consider the development of the limit in base $2$. Is it periodic?
– Jean-Claude Arbaut
Nov 23 at 22:39
showing it is even transcendental should not be too hard, given that it has so good approximations
– Hagen von Eitzen
Nov 23 at 22:57
What makes you think that?
– user1892304
Nov 23 at 22:30
What makes you think that?
– user1892304
Nov 23 at 22:30
1
1
You are asking different thing in the post from the title.
– user587192
Nov 23 at 22:31
You are asking different thing in the post from the title.
– user587192
Nov 23 at 22:31
Sorry, I fixed it now.
– You Zhou
Nov 23 at 22:38
Sorry, I fixed it now.
– You Zhou
Nov 23 at 22:38
1
1
Consider the development of the limit in base $2$. Is it periodic?
– Jean-Claude Arbaut
Nov 23 at 22:39
Consider the development of the limit in base $2$. Is it periodic?
– Jean-Claude Arbaut
Nov 23 at 22:39
showing it is even transcendental should not be too hard, given that it has so good approximations
– Hagen von Eitzen
Nov 23 at 22:57
showing it is even transcendental should not be too hard, given that it has so good approximations
– Hagen von Eitzen
Nov 23 at 22:57
add a comment |
1 Answer
1
active
oldest
votes
up vote
3
down vote
accepted
The binary representation $0.01010001cdots$ doesn't terminate or repeat.
answered Nov 23 at 22:45
J.G.
19.6k21932
add a comment |
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
3
down vote
accepted
The binary representation $0.01010001cdots$ doesn't terminate or repeat.
answered Nov 23 at 22:45
J.G.
19.6k21932
add a comment |
up vote
3
down vote
accepted
The binary representation $0.01010001cdots$ doesn't terminate or repeat.
answered Nov 23 at 22:45
J.G.
19.6k21932
add a comment |
up vote
3
down vote
accepted
up vote
3
down vote
accepted
The binary representation $0.01010001cdots$ doesn't terminate or repeat.
answered Nov 23 at 22:45
J.G.
19.6k21932
The binary representation $0.01010001cdots$ doesn't terminate or repeat.
answered Nov 23 at 22:45
J.G.
19.6k21932
answered Nov 23 at 22:45
J.G.
19.6k21932
answered Nov 23 at 22:45
J.G.
19.6k21932
answered Nov 23 at 22:45
J.G.
19.6k21932
19.6k21932
add a comment |
add a comment |
What makes you think that?
– user1892304
Nov 23 at 22:30
1
You are asking different thing in the post from the title.
– user587192
Nov 23 at 22:31
Sorry, I fixed it now.
– You Zhou
Nov 23 at 22:38
1
Consider the development of the limit in base $2$. Is it periodic?
– Jean-Claude Arbaut
Nov 23 at 22:39
showing it is even transcendental should not be too hard, given that it has so good approximations
– Hagen von Eitzen
Nov 23 at 22:57