Panphobia said:
I like $$e=\sum_{n\geq 0}f(n),$$ where ##\displaystyle f(n)=\left\{\begin{matrix}e & \text{if } n=0 \\ 0 & \text{if } n\neq 0\end{matrix}\right.##. :tongue:mesa said:I honestly don't know how you guys find so much more on Wikipedia than I do...
Either way, that is an excellent list of 'infinite series', are there any others?
Mandelbroth said:I like $$e=\sum_{n\geq 0}f(n),$$ where ##\displaystyle f(n)=\left\{\begin{matrix}e & \text{if } n=0 \\ 0 & \text{if } n\neq 0\end{matrix}\right.##. :tongue:
Personally, I prefer $$e=\sum_{n\geq 0}f(n),$$ where ##\displaystyle f(n)=\left\{\begin{matrix}e & \text{if } n=1 \\ 0 & \text{if } n\neq 1\end{matrix}\right.##Mandelbroth said:I like $$e=\sum_{n\geq 0}f(n),$$ where ##\displaystyle f(n)=\left\{\begin{matrix}e & \text{if } n=0 \\ 0 & \text{if } n\neq 0\end{matrix}\right.##. :tongue:
Do you honestly think we know all of mathematics?mesa said:So is this all of them, as in if someone found something else outside of these then it's new to maths?
Mandelbroth said:Do you honestly think we know all of mathematics?...
That list is not exhaustive. There is, as far as I know, not much interest in simply finding new infinite series that add up to 'e,' except perhaps if a new series converges much more rapidly than a previously known series.mesa said:Nope, just trying to see if someone else has more information. Do you have recommendations on where to find out more on the subject such as books, websites, etc.?
Jorriss said:That list is not exhaustive. There is, as far as I know, not much interest in simply finding new infinite series that add up to 'e,' except perhaps if a new series converges much more rapidly than a previously known series.
In what sense valuable? I do not believe there is much interest in finding more decimal places to e beyond the novelty of having found new decimals - though someone more knowledgeable can certainly correct me.mesa said:I would imagine that would be valuable from a computing standpoint. What's the current record, 10 trillion decimal places or something to that effect?
mesa said:Do you have recommendations on where to find out more on the subject such as books, websites, etc.?
Jorriss said:In what sense valuable? I do not believe there is much interest in finding more decimal places to e beyond the novelty of having found new decimals - though someone more knowledgeable can certainly correct me.
Stephen Tashi said:Why not concentrate on finding infinite series that sum to [itex] 1 [/itex] and then multiply them by [itex] e [/itex]? That would let you find series that sum to [itex] \pi [/itex] or [itex] 42 [/itex] or whatever.
'e' is a mathematical constant that is approximately equal to 2.71828. It is the base of the natural logarithm and is important in many mathematical and scientific calculations, such as compound interest, population growth, and radioactive decay.
An infinite series is a sum of an infinite number of terms. Each term in the series is added to the previous term, and the sum of all the terms is the infinite series.
'e' can be expressed as an infinite series, specifically the sum of 1/n!, where n ranges from 0 to infinity. This series converges to 'e' and is known as the Taylor series for 'e'.
One example is the infinite series 1 + 1/1! + 1/2! + 1/3! + ... which is equal to 'e'.
Yes, there are many other infinite series that converge to 'e', such as 1 + 1/2 + 1/4 + 1/8 + ... and 2 - 1 + 1/2 - 1/3 + 1/4 - 1/5 + ... These series are derived from different mathematical concepts, such as geometric and harmonic series.