Question

Found an interesting formula for calculating nth digit of pi

Answer 1

\[\sum_{\infty}^{n=0}[\frac{ 4 }{ 8n+1 }-\frac{ 2 }{ 8n+4 }-\frac{ 1 }{ 8n+5 }-\frac{ 1 }{ 8n+6 }]\left( \frac{ 1 }{ 16 } \right)^{n}\]

Answer 2

well thats a great achievment man !

Answer 3

wow, lets check its true for n=1 :)

Answer 4

ok

Answer 5

okay so tell me what the 10 billionth digit of pi is

Answer 6

you probably cant prove this is true using induction

Answer 7

i would like to simplify this formula, using common denominator, one sec

Answer 8

yes, it is 4 now check it lol

Answer 9

Sum (120*n^2+151*n+47)/((8*n+1)*(2*n+1)*(8*n+5)*(4*n+3)*16^n) , n=0..oo

Answer 10

so it is coming 3?

Answer 11

one moment, getting calculator

Answer 12

wolfram!

Answer 13

at n=0 we have 3.133

Answer 14

oh ok, the 'nth' digit of pi does work

Answer 15

yes it works

Answer 16

are you sure it does ?

Answer 17

this is a very interesting formula to generate the nth digit of pi. and the sum of this is pi, according to maple

Answer 18

I mean other formulas to generate pi will not give you exactly the nth digit of pi. such as the power series of 4*arctan (1)

Answer 19

also make sure reader knows, you are counting from zero, so the 'first' digit of pi corresponds to n=0 , second digit of pi corresponds to n=1

Answer 20

so the 'zeroth' digit of pi is 3, the 'first' digit of pi is 1, etc

Answer 21

yessss ya

Answer 22

do you know how the number pi is actually generated in a computer?

Answer 23

It's just a ratio of circumference and diameter , so take a circle with known diameter and compute

Answer 24

lol for that you have to know pi lol -_-

Answer 25

it's a series representation
Technically, yes, it's a formula for calculating the nth digit of pi
But what this means, is that if you take enough terms in the series, you'll get an accurate estimate of pi to the nth digit
It's not the same thing as closed formula for the n-th digit of pi
That actually would be an amazing mathematical find... quite amazing

Answer 26

One could make a hobby out of finding representations of Pi

Answer 27

http://functions.wolfram.com/Constants/Pi/06/01/01/

Answer 28

There are different people who tried to find such formulas
Yes, there are people who have world records in reciting pi

World record is reciting 25464 digits of pi, took 5.5 hours to recite

Answer 29

There is this one with arctan and the fibonacci numbers
Interesting...

Answer 30

there is a taylor formula for this too

Answer 31

cool :)

Answer 32

Is that Daniel Tammet?

Answer 33

who holds the record

Answer 34

Probably , i saw his interview in David Letterman show

Answer 35

well , the most amazing thing that u might find is
knowing the n digit it self ... not a seriese for all pi
if someone found that ,then its amazing else it means nothing :D
(at least for me :P)

Answer 36

Yes, in fact, I think he actually knows it to more digits, but it's how many can you recite in the given time

It's actually very exhausting to recite that many digits in the given time... it's like speaking incessantly for hours

Answer 37

the human computer sweats :)

Answer 38

He is a SAVANT.

Answer 39

I always wanted Kim Peek's ability to read two pages at once and near perfect recall. Because of the separation between the left/right hemispheres of his brain. He could read the left page with one eye, and the right page with the other. Amazing.

Answer 40

i think daniel temmet might be a fraud