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Interesting, useless mathematical series

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Rudin
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04 Sep 2015, 6:13 pm

Here is a few useless but fascinating mathematical series that I decided to share with you. Will they ever be useful? Not likely, but are they interesting? Indubitably.

Image

Image

Image

Image

Image

I believe this one is Newton's binomial theorem:

Image


Please post series you deem interesting in this thread.

~~~Rudin~~~


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Rudin
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04 Sep 2015, 6:14 pm

I forgot a complicated one, that I think is interesting.

Image


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"God may not play dice with the universe, but something strange is going on with prime numbers."

-Paul Erdos

"There are two types of cryptography in this world: cryptography that will stop your kid sister from looking at your files, and cryptography that will stop major governments from reading your files."

-Bruce Schneider


Rudin
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10 Sep 2015, 6:36 pm

Bump


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"God may not play dice with the universe, but something strange is going on with prime numbers."

-Paul Erdos

"There are two types of cryptography in this world: cryptography that will stop your kid sister from looking at your files, and cryptography that will stop major governments from reading your files."

-Bruce Schneider


Rudin
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10 Sep 2015, 6:37 pm

Bump


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"God may not play dice with the universe, but something strange is going on with prime numbers."

-Paul Erdos

"There are two types of cryptography in this world: cryptography that will stop your kid sister from looking at your files, and cryptography that will stop major governments from reading your files."

-Bruce Schneider


Rudin
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10 Sep 2015, 6:39 pm

Sorry for bumping but no one is sharing.


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"God may not play dice with the universe, but something strange is going on with prime numbers."

-Paul Erdos

"There are two types of cryptography in this world: cryptography that will stop your kid sister from looking at your files, and cryptography that will stop major governments from reading your files."

-Bruce Schneider


Nuthatchnut
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13 Sep 2015, 3:46 pm

Don't have one to share, but I can give you a bump.


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Nuthatchnut
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14 Sep 2015, 1:59 pm

Not sure if this is what you are looking for.
I am fond of the near-perfect imperfection that is the spiral of Theodorus.

This is Philip J. Davis' solution to making a smooth curve out of it:
Image


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eric76
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14 Sep 2015, 2:11 pm

Why do you think they are useless?



eric76
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14 Sep 2015, 2:13 pm

For a series that may actually be useless, sum the squares of all positive integers to the 100th power.

1+2^100+3^100+4^100+...



Rudin
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14 Sep 2015, 4:58 pm

eric76 wrote:
Why do you think they are useless?


Some of them are useful like Newton's Binomial Theorem. Most of them have no further contribution in mathematics.


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"God may not play dice with the universe, but something strange is going on with prime numbers."

-Paul Erdos

"There are two types of cryptography in this world: cryptography that will stop your kid sister from looking at your files, and cryptography that will stop major governments from reading your files."

-Bruce Schneider


Rudin
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14 Sep 2015, 5:06 pm

eric76 wrote:
For a series that may actually be useless, sum the squares of all positive integers to the 100th power.

1+2^100+3^100+4^100+...


Here is the partial sum result. Image


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"God may not play dice with the universe, but something strange is going on with prime numbers."

-Paul Erdos

"There are two types of cryptography in this world: cryptography that will stop your kid sister from looking at your files, and cryptography that will stop major governments from reading your files."

-Bruce Schneider