OOPS, the results printed by that BASIC program are wrong:

>Maybe I'm just pointing out the obvious, but it seems to me that the
algorithm to generate that series (or any series not involving negative
coefficients for any of the terms) can easily be generated by the simple
algorithm:
>
>CLS
>b = 1 / 3      ' The required fraction
>tol = .0001   ' As needed
>a = 0
>d = .5
>d2 = 2
>WHILE ABS(a - b) > tol
>c = a + d
>d = d / 2
>'d2 = d2 * 2 ' **** THIS LINE SHOULD GO AFTER THE NEXT
>IF c <= b THEN a = c: PRINT "1/"; d2 ' This term is included, so print it out
d2 = d2 * 2  ' **** RIGHT HERE
>WEND
>
>Sean
>
>
>
>At 10:59 PM 7/24/99 -0700, you wrote:
>>>I had this gut feeling that the series Myke listed had
>>>popped out of an Euler transformation somehow, and I was
>>>fooling around with that. What I noticed, however, was that
>>>if the Euler transformation was applied backward of what
>>>I had first thought (and I'm not this smart, this is an
>>>immediate consequence of a derivaton in R.W. Hamming's
>>>book on Numerical Methods, section 12.6, on page 203 of
>>>the Dover edition), that you can improve the convergence
>>>of such a series while still working exclusively with
>>>powers of two. In particular, the series
>>
>>>  1/2 * ( 1/4 + 1/16 + 1/64 + 1/256 + ... + 1/(4^n) + ... )
>>
>>>Also converges to 1/3, but at a much quicker rate.
>>>I calculated the two series in Excel to demonstrate:
>
|
| Sean Breheny
| Amateur Radio Callsign: KA3YXM
| Electrical Engineering Student
\--------------=----------------
Save lives, please look at http://www.all.org
Personal page: http://www.people.cornell.edu/pages/shb7
mailto:shb7@cornell.edu ICQ #: 3329174
________________________________________________________
NetZero - We believe in a FREE Internet.  Shouldn't you?
Get your FREE Internet Access and Email at
http://www.netzero.net/download/index.html