Solving Pi

[John Collins]

In article <11307 at watnot.UUCP> cagordon at watnot.UUCP (Chris A. Gordon) writes:
>Here is a more simple sum-evaluation of pi (thought I don't know if it will
>work with the original program):
>
>               oo
>              ----         k-1
>         |  | \        (-1)
>    pi = +--+  >    ----------
>	    | /       2k-1
>	      ----
>	      k=1

The convergence of this series is *TERRIBLE* You'd have to evaluate many
thousands of terms to get anywhere (you are still messing around with the
third decimal place after 500 terms!).

Moreover the alternation of the signs makes life even more difficult -
each term cancels most of the work of the previous term.

Use of Aitken acceleration has a dramatic improvement though - but the
resulting series can be shown to be equivalent to the series for

		6 * arcsin(.5)

which was given in a previous message.
-- 
John M Collins		....mcvax!ist!inset!jmc
Phone:	+44 727 57267
Snail Mail: 47 Cedarwood Drive, St Albans, Herts, AL4 0DN, England.