Mixing
Evaluation of $sum_{p text{ is a prime }}frac{1}{p!}$
$begingroup$
I apologize in advance, if these have been posted earlier (as I couldn't find them).
While surfing through the Internet, I came across the following problem:
Evaluate: $displaystylesum_{n=0}^{infty} frac{1}{(3n)!}$,
which I computed successfully by using roots of unity filter.
After a little while I became a bit curious and wondered how to compute the following series: $displaystylesum_{p text{ is a prime }}frac{1}{p!}$.
My first idea was to use sieve of erasthosthenes along with roots of unity filter but I can't figure out how to do so.
Questions similar to these are also coming to my mind, which I have no idea on how to approach to, like $sum_{n=0}^{infty}frac{1}{(n^2)!}$, etc.
If possible, please provide me little hints on how to proceed.
Thanks.
real-analysis sequences-and-series
edited Jan 25 at 17:02
Namaste
1
asked Jan 25 at 16:46
himanshu mallickhimanshu mallick
365
$endgroup$
add a comment |
$begingroup$
I apologize in advance, if these have been posted earlier (as I couldn't find them).
While surfing through the Internet, I came across the following problem:
Evaluate: $displaystylesum_{n=0}^{infty} frac{1}{(3n)!}$,
which I computed successfully by using roots of unity filter.
After a little while I became a bit curious and wondered how to compute the following series: $displaystylesum_{p text{ is a prime }}frac{1}{p!}$.
My first idea was to use sieve of erasthosthenes along with roots of unity filter but I can't figure out how to do so.
Questions similar to these are also coming to my mind, which I have no idea on how to approach to, like $sum_{n=0}^{infty}frac{1}{(n^2)!}$, etc.
If possible, please provide me little hints on how to proceed.
Thanks.
real-analysis sequences-and-series
edited Jan 25 at 17:02
Namaste
1
asked Jan 25 at 16:46
himanshu mallickhimanshu mallick
365
$endgroup$
1
$begingroup$
I highly doubt either $sum_p1/p$ or $sum_n1/(n^2)!$ has a sensible closed form.
$endgroup$
– Wojowu
Jan 25 at 16:53
$begingroup$
@JackD'Aurizio Forgot an exclamation mark!
$endgroup$
– Wojowu
Jan 25 at 17:21
add a comment |
$begingroup$
I apologize in advance, if these have been posted earlier (as I couldn't find them).
While surfing through the Internet, I came across the following problem:
Evaluate: $displaystylesum_{n=0}^{infty} frac{1}{(3n)!}$,
which I computed successfully by using roots of unity filter.
After a little while I became a bit curious and wondered how to compute the following series: $displaystylesum_{p text{ is a prime }}frac{1}{p!}$.
My first idea was to use sieve of erasthosthenes along with roots of unity filter but I can't figure out how to do so.
Questions similar to these are also coming to my mind, which I have no idea on how to approach to, like $sum_{n=0}^{infty}frac{1}{(n^2)!}$, etc.
If possible, please provide me little hints on how to proceed.
Thanks.
real-analysis sequences-and-series
edited Jan 25 at 17:02
Namaste
1
asked Jan 25 at 16:46
himanshu mallickhimanshu mallick
365
$endgroup$
I apologize in advance, if these have been posted earlier (as I couldn't find them).
While surfing through the Internet, I came across the following problem:
Evaluate: $displaystylesum_{n=0}^{infty} frac{1}{(3n)!}$,
which I computed successfully by using roots of unity filter.
After a little while I became a bit curious and wondered how to compute the following series: $displaystylesum_{p text{ is a prime }}frac{1}{p!}$.
My first idea was to use sieve of erasthosthenes along with roots of unity filter but I can't figure out how to do so.
Questions similar to these are also coming to my mind, which I have no idea on how to approach to, like $sum_{n=0}^{infty}frac{1}{(n^2)!}$, etc.
If possible, please provide me little hints on how to proceed.
Thanks.
real-analysis sequences-and-series
real-analysis sequences-and-series
edited Jan 25 at 17:02
Namaste
1
asked Jan 25 at 16:46
himanshu mallickhimanshu mallick
365
edited Jan 25 at 17:02
Namaste
1
asked Jan 25 at 16:46
himanshu mallickhimanshu mallick
365
edited Jan 25 at 17:02
Namaste
1
edited Jan 25 at 17:02
Namaste
1
edited Jan 25 at 17:02
Namaste
1
1
asked Jan 25 at 16:46
himanshu mallickhimanshu mallick
365
asked Jan 25 at 16:46
himanshu mallickhimanshu mallick
365
asked Jan 25 at 16:46
himanshu mallickhimanshu mallick
365
365
1
$begingroup$
I highly doubt either $sum_p1/p$ or $sum_n1/(n^2)!$ has a sensible closed form.
$endgroup$
– Wojowu
Jan 25 at 16:53
$begingroup$
@JackD'Aurizio Forgot an exclamation mark!
$endgroup$
– Wojowu
Jan 25 at 17:21
add a comment |
1
$begingroup$
I highly doubt either $sum_p1/p$ or $sum_n1/(n^2)!$ has a sensible closed form.
$endgroup$
– Wojowu
Jan 25 at 16:53
$begingroup$
@JackD'Aurizio Forgot an exclamation mark!
$endgroup$
– Wojowu
Jan 25 at 17:21
1
1
$begingroup$
I highly doubt either $sum_p1/p$ or $sum_n1/(n^2)!$ has a sensible closed form.
$endgroup$
– Wojowu
Jan 25 at 16:53
$begingroup$
I highly doubt either $sum_p1/p$ or $sum_n1/(n^2)!$ has a sensible closed form.
$endgroup$
– Wojowu
Jan 25 at 16:53
$begingroup$
@JackD'Aurizio Forgot an exclamation mark!
$endgroup$
– Wojowu
Jan 25 at 17:21
$begingroup$
@JackD'Aurizio Forgot an exclamation mark!
$endgroup$
– Wojowu
Jan 25 at 17:21
add a comment |
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1
$begingroup$
I highly doubt either $sum_p1/p$ or $sum_n1/(n^2)!$ has a sensible closed form.
$endgroup$
– Wojowu
Jan 25 at 16:53
$begingroup$
@JackD'Aurizio Forgot an exclamation mark!
$endgroup$
– Wojowu
Jan 25 at 17:21