Can we find the exact sum of series $sum_{n=0}^infty frac{1}{(n!)^n}$ [on hold]Find the Exact sumFinding sum...

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Can we find the exact sum of series $sum_{n=0}^infty frac{1}{(n!)^n}$ [on hold]


Find the Exact sumFinding sum of the power series and the sum of the seriesFind the sum of $sum_{n=1}^{infty}frac{n}{x^n}$Which (convergent) series can one find the sum of?How to calculate this sum : $sum_ {n=0}^{+infty} frac{1}{8^n(3n+1)}$Find the sum of the series $sum_{k=1}^infty frac{(-1)^{k-1}}{2^kk}$Find the sum of the power series $sumlimits_{n=1}^infty frac{(n+2)!}{(2!)(n!)}x^n$Examine the convergence and find the sum of series $sum_{n=1}^{infty}(-1)^nfrac{(2n-1)!!}{(2n)!!}.$Find the sum of the series $sum_{n=1}^{infty}frac{1}{2^n-1}.$How to find the exact value of $sum _{n=2}^{infty }:frac{2^{n+1}}{left(n+1right)3^n}$













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$begingroup$


Can we find the exact sum of series $sum_{n=0}^infty frac{1}{(n!)^n}$?



We know thaf the sum is $e$ without that power 'n' in the denominator.










share|cite|improve this question









$endgroup$



put on hold as off-topic by Eevee Trainer, RRL, John Omielan, Leucippus, Alex Provost yesterday


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 provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Eevee Trainer, RRL, John Omielan, Leucippus, Alex Provost

If this question can be reworded to fit the rules in the help center, please edit the question.












  • 2




    $begingroup$
    This converges very fast, so you can compute it numerically. Then put the digits into OEIS to see if there is any information.
    $endgroup$
    – Jair Taylor
    yesterday






  • 2




    $begingroup$
    @JairTaylor Which brings one to this page.
    $endgroup$
    – Servaes
    yesterday












  • $begingroup$
    So we only see the numerical value there
    $endgroup$
    – ersh
    yesterday










  • $begingroup$
    By the way, I already know this series converges to an irrational number.
    $endgroup$
    – ersh
    yesterday
















1












$begingroup$


Can we find the exact sum of series $sum_{n=0}^infty frac{1}{(n!)^n}$?



We know thaf the sum is $e$ without that power 'n' in the denominator.










share|cite|improve this question









$endgroup$



put on hold as off-topic by Eevee Trainer, RRL, John Omielan, Leucippus, Alex Provost yesterday


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 provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Eevee Trainer, RRL, John Omielan, Leucippus, Alex Provost

If this question can be reworded to fit the rules in the help center, please edit the question.












  • 2




    $begingroup$
    This converges very fast, so you can compute it numerically. Then put the digits into OEIS to see if there is any information.
    $endgroup$
    – Jair Taylor
    yesterday






  • 2




    $begingroup$
    @JairTaylor Which brings one to this page.
    $endgroup$
    – Servaes
    yesterday












  • $begingroup$
    So we only see the numerical value there
    $endgroup$
    – ersh
    yesterday










  • $begingroup$
    By the way, I already know this series converges to an irrational number.
    $endgroup$
    – ersh
    yesterday














1












1








1


1



$begingroup$


Can we find the exact sum of series $sum_{n=0}^infty frac{1}{(n!)^n}$?



We know thaf the sum is $e$ without that power 'n' in the denominator.










share|cite|improve this question









$endgroup$




Can we find the exact sum of series $sum_{n=0}^infty frac{1}{(n!)^n}$?



We know thaf the sum is $e$ without that power 'n' in the denominator.







real-analysis calculus algebraic-number-theory irrational-numbers






share|cite|improve this question













share|cite|improve this question











share|cite|improve this question




share|cite|improve this question










asked yesterday









ershersh

431113




431113




put on hold as off-topic by Eevee Trainer, RRL, John Omielan, Leucippus, Alex Provost yesterday


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 provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Eevee Trainer, RRL, John Omielan, Leucippus, Alex Provost

If this question can be reworded to fit the rules in the help center, please edit the question.







put on hold as off-topic by Eevee Trainer, RRL, John Omielan, Leucippus, Alex Provost yesterday


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 provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Eevee Trainer, RRL, John Omielan, Leucippus, Alex Provost

If this question can be reworded to fit the rules in the help center, please edit the question.








  • 2




    $begingroup$
    This converges very fast, so you can compute it numerically. Then put the digits into OEIS to see if there is any information.
    $endgroup$
    – Jair Taylor
    yesterday






  • 2




    $begingroup$
    @JairTaylor Which brings one to this page.
    $endgroup$
    – Servaes
    yesterday












  • $begingroup$
    So we only see the numerical value there
    $endgroup$
    – ersh
    yesterday










  • $begingroup$
    By the way, I already know this series converges to an irrational number.
    $endgroup$
    – ersh
    yesterday














  • 2




    $begingroup$
    This converges very fast, so you can compute it numerically. Then put the digits into OEIS to see if there is any information.
    $endgroup$
    – Jair Taylor
    yesterday






  • 2




    $begingroup$
    @JairTaylor Which brings one to this page.
    $endgroup$
    – Servaes
    yesterday












  • $begingroup$
    So we only see the numerical value there
    $endgroup$
    – ersh
    yesterday










  • $begingroup$
    By the way, I already know this series converges to an irrational number.
    $endgroup$
    – ersh
    yesterday








2




2




$begingroup$
This converges very fast, so you can compute it numerically. Then put the digits into OEIS to see if there is any information.
$endgroup$
– Jair Taylor
yesterday




$begingroup$
This converges very fast, so you can compute it numerically. Then put the digits into OEIS to see if there is any information.
$endgroup$
– Jair Taylor
yesterday




2




2




$begingroup$
@JairTaylor Which brings one to this page.
$endgroup$
– Servaes
yesterday






$begingroup$
@JairTaylor Which brings one to this page.
$endgroup$
– Servaes
yesterday














$begingroup$
So we only see the numerical value there
$endgroup$
– ersh
yesterday




$begingroup$
So we only see the numerical value there
$endgroup$
– ersh
yesterday












$begingroup$
By the way, I already know this series converges to an irrational number.
$endgroup$
– ersh
yesterday




$begingroup$
By the way, I already know this series converges to an irrational number.
$endgroup$
– ersh
yesterday










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