Welcome to NRICH.

 
Pi's value as an infinite series
By Zhidong Leong on Sunday, July 22, 2001 - 02:18 pm:

I remember that pi's value is a infinite series.
But how to prove that?

By Arun Iyer on Tuesday, July 24, 2001 - 09:10 pm:

Well,
the series for arctan is
arctan(x) = x - x3/3 + x5/5 - x7/7 + x9/9 - ......

putting x=1 we get,
arctan(1) = 1 - 1/3 + 1/5 - 1/7 + 1/9 - ....

but arctan(1)=p/4
hence,
p/4 = 1 - 1/3 + 1/5 - 1/7 + 1/9 - ....

hence,
p = 4 - 4/3 + 4/5 - 4/7 + 4/9 - ....

I hope this is what you asked for!!!

love arun