Pi/AConvergentSeries

A Challenge

R.E. Boss posted the following challenge to the J Programming Forum. Unfortunately, I was unable to access the link he provided, so I've included what I think is the relevant portion below in the section The Series.

from:	 R.E. Boss r.e.boss@planet.nl via srs.acm.org
to:	 Programming forum <programming@jsoftware.com>
date:	 Mon, May 14, 2012 at 5:02 AM
subject: [Jprogramming] Challenge 12(?)

I scanned a part of Exploratory Experimentation and Computation, https://www.opendrive.com/files?57384074_sCfMP , where two statements are made about a very rapidly convergent series.

1. The first term coincides with (pi % 8) in the first 42 digits
2. The first 2 terms even give 500 digits

How can these two statements be confirmed (or rejected) with J?

(No deadlines apply.)

R.E. Boss

The Series

From this PDF on the website of the AMS (American Mathematical Society):