# Thread: Finding pi as a sum of rational number :]

1. ## Finding pi as a sum of rational number :]

Well I'm abit curious about the Taylor Series-

Suppose f(x)= arctan(x)

Lets find the taylor series of f(x)....

We get that

arctan(x)= SUM n=0 --> infinity [x- x^3/3 + x^5/5 -x^7/7 ..... (-1)^(n+1)*x^(n+1) / (n+1) .......... ]

lets assume that its keeps going and there is no end point k

when we sub in x=1

we get

pi/4= 1-1/3+1/5+1/7 + .................+ 1/(n+2) +.........

now multiply both by 4

we should get pi is approx = 4 -4/3 +4/5 +4/7 ............. + 4/(n+2) +.....

Is this enough ??

is there a proof where it shows pi can be written in rational/irrational numbers etc..

I know my proof seems sort of dodgy- but please correct me

Thanks for your time and effort.

2. you made a typo with -4/2 as it should be -4/3 but otherwise

Leibniz formula for pi - Wikipedia, the free encyclopedia

your proof is certainly convincing enough even if not as rigorous as it could be

3. Originally Posted by Khonics89
Well I'm abit curious about the Taylor Series-

Suppose f(x)= arctan(x)

Lets find the taylor series of f(x)....

We get that

arctan(x)= SUM n=0 --> infinity [x- x^3/3 + x^5/5 -x^7/7 ..... (-1)^(n+1)*x^(n+1) / (n+1) .......... ]

lets assume that its keeps going and there is no end point k

when we sub in x=1

we get

pi/4= 1-1/3+1/5+1/7 + .................+ 1/(n+2) +.........

now multiply both by 4

we should get pi is approx = 4 -4/2 +4/5 +4/7 ............. + 4/(n+2) +.....

Is this enough ??

is there a proof where it shows pi can be written in rational/irrational numbers etc..

I know my proof seems sort of dodgy- but please correct me

Thanks for your time and effort.
Pi - Wikipedia, the free encyclopedia

4. ohh ok nice websites