What is the name of this series test?
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Theorem: Suppose $a_1ge a_2ge a_3gecdotsge0$. Then, $sum_{n=1}^{infty}a_n$ converges iff $sum_{k=0}^{infty}2^ka_{2^k}=a_1+2a_2+4a_4+8a_8+cdots$ converges.
I've taken to calling it the "Companion Test", but I'm sure there's a proper name for it.
sequences-and-series convergence terminology
edited Dec 14 '18 at 23:49
timtfj
2,198420
asked Dec 14 '18 at 19:17
TreeTree
1046
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add a comment |
$begingroup$
Theorem: Suppose $a_1ge a_2ge a_3gecdotsge0$. Then, $sum_{n=1}^{infty}a_n$ converges iff $sum_{k=0}^{infty}2^ka_{2^k}=a_1+2a_2+4a_4+8a_8+cdots$ converges.
I've taken to calling it the "Companion Test", but I'm sure there's a proper name for it.
sequences-and-series convergence terminology
edited Dec 14 '18 at 23:49
timtfj
2,198420
asked Dec 14 '18 at 19:17
TreeTree
1046
$endgroup$
$begingroup$
This is a totally clear and specific question—I find the downvote very odd.
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– timtfj
Dec 14 '18 at 23:27
add a comment |
$begingroup$
Theorem: Suppose $a_1ge a_2ge a_3gecdotsge0$. Then, $sum_{n=1}^{infty}a_n$ converges iff $sum_{k=0}^{infty}2^ka_{2^k}=a_1+2a_2+4a_4+8a_8+cdots$ converges.
I've taken to calling it the "Companion Test", but I'm sure there's a proper name for it.
sequences-and-series convergence terminology
edited Dec 14 '18 at 23:49
timtfj
2,198420
asked Dec 14 '18 at 19:17
TreeTree
1046
$endgroup$
Theorem: Suppose $a_1ge a_2ge a_3gecdotsge0$. Then, $sum_{n=1}^{infty}a_n$ converges iff $sum_{k=0}^{infty}2^ka_{2^k}=a_1+2a_2+4a_4+8a_8+cdots$ converges.
I've taken to calling it the "Companion Test", but I'm sure there's a proper name for it.
sequences-and-series convergence terminology
sequences-and-series convergence terminology
edited Dec 14 '18 at 23:49
timtfj
2,198420
asked Dec 14 '18 at 19:17
TreeTree
1046
edited Dec 14 '18 at 23:49
timtfj
2,198420
asked Dec 14 '18 at 19:17
TreeTree
1046
edited Dec 14 '18 at 23:49
timtfj
2,198420
edited Dec 14 '18 at 23:49
timtfj
2,198420
edited Dec 14 '18 at 23:49
timtfj
2,198420
2,198420
asked Dec 14 '18 at 19:17
TreeTree
1046
asked Dec 14 '18 at 19:17
TreeTree
1046
asked Dec 14 '18 at 19:17
TreeTree
1046
1046
$begingroup$
This is a totally clear and specific question—I find the downvote very odd.
$endgroup$
– timtfj
Dec 14 '18 at 23:27
add a comment |
$begingroup$
This is a totally clear and specific question—I find the downvote very odd.
$endgroup$
– timtfj
Dec 14 '18 at 23:27
$begingroup$
This is a totally clear and specific question—I find the downvote very odd.
$endgroup$
– timtfj
Dec 14 '18 at 23:27
$begingroup$
This is a totally clear and specific question—I find the downvote very odd.
$endgroup$
– timtfj
Dec 14 '18 at 23:27
add a comment |
1 Answer
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It is called the Cauchy Condensation Test.
answered Dec 14 '18 at 19:18
GenericMathGuyGenericMathGuy
1312
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1 Answer
1
active
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1 Answer
1
active
oldest
votes
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active
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votes
$begingroup$
It is called the Cauchy Condensation Test.
answered Dec 14 '18 at 19:18
GenericMathGuyGenericMathGuy
1312
$endgroup$
add a comment |
$begingroup$
It is called the Cauchy Condensation Test.
answered Dec 14 '18 at 19:18
GenericMathGuyGenericMathGuy
1312
$endgroup$
add a comment |
$begingroup$
It is called the Cauchy Condensation Test.
answered Dec 14 '18 at 19:18
GenericMathGuyGenericMathGuy
1312
$endgroup$
It is called the Cauchy Condensation Test.
answered Dec 14 '18 at 19:18
GenericMathGuyGenericMathGuy
1312
answered Dec 14 '18 at 19:18
GenericMathGuyGenericMathGuy
1312
answered Dec 14 '18 at 19:18
GenericMathGuyGenericMathGuy
1312
answered Dec 14 '18 at 19:18
GenericMathGuyGenericMathGuy
1312
1312
add a comment |
add a comment |
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$begingroup$
This is a totally clear and specific question—I find the downvote very odd.
$endgroup$
– timtfj
Dec 14 '18 at 23:27