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







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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
















2












$begingroup$


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







share|cite|improve this question











$endgroup$












  • $begingroup$
    This is a totally clear and specific question—I find the downvote very odd.
    $endgroup$
    – timtfj
    Dec 14 '18 at 23:27














2












2








2





$begingroup$


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







share|cite|improve this question











$endgroup$




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






share|cite|improve this question















share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited Dec 14 '18 at 23:49









timtfj

2,198420




2,198420










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


















  • $begingroup$
    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










1 Answer
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It is called the Cauchy Condensation Test.






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    $begingroup$

    It is called the Cauchy Condensation Test.






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      6












      $begingroup$

      It is called the Cauchy Condensation Test.






      share|cite|improve this answer









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        6












        6








        6





        $begingroup$

        It is called the Cauchy Condensation Test.






        share|cite|improve this answer









        $endgroup$



        It is called the Cauchy Condensation Test.







        share|cite|improve this answer












        share|cite|improve this answer



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        answered Dec 14 '18 at 19:18









        GenericMathGuyGenericMathGuy

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