User:Jaume Oliver Lafont/Pi supertask

Accelerating convergence?

Let us compute Pi/4 through the following procedure.

The cumulated sum s(t) is zero for t<0.

At time t=1-2^(-n) add (-1)^n/(2n+1) to s, for all nonnegative integers n.

What can be said about s(1)? Does s(1) equal Pi/4? If not, is it smaller than Pi/4? Is it greater? Undefined?

http://en.wikipedia.org/wiki/Supertask