Agree, very nice solution Raul. > On 13 Mar 2016, at 10:02 AM, Kip Murray <[email protected]> wrote: > > Very nice, Raul! Much shorter than my Rube Goldberg approach. --Kip > > On Saturday, March 12, 2016, Raul Miller <[email protected]> wrote: > >> cv=: ([: (+`%/) 1 }.,)\@|: >> >> I hope this helps... >> >> -- >> Raul >> >> >> On Sat, Mar 12, 2016 at 1:21 PM, Kip Murray <[email protected] >> <javascript:;>> wrote: >>> Here you go: >>> >>> nume =: 1 , 1 % 4x * _1 + 4 * [: *:@>:@i. <: >>> >>> dene =: 1 1r2 , 1 $~ _2 + ] >>> >>> I think I got those from Abramowitz and Stegun. >>> >>> (_1 , nume 6),: dene 7 >>> _1 1 1r12 1r60 1r140 1r252 1r396 >>> 1 1r2 1 1 1 1 1 >>> >>> --Kip >>> >>> >>> On Saturday, March 12, 2016, Raul Miller <[email protected] >> <javascript:;>> wrote: >>> >>>> How do you compute the first two rows? >>>> >>>> Thanks, >>>> >>>> -- >>>> Raul >>>> >>>> On Saturday, March 12, 2016, Kip Murray <[email protected] >> <javascript:;> >>>> <javascript:;>> wrote: >>>> >>>>> The challenge is at the end. First a table for a finite continued >>>> fraction >>>>> that approximates e =: ^ 1 . >>>>> --Kip Murray >>>>> >>>>> >>>>> The table below summarizes a finite continued fraction which begins >>>>> >>>>> 1 >>>>> 1 + ------------- >>>>> 1r12 >>>>> 1r2 + -------- >>>>> 1r60 >>>>> 1 + ------ >>>>> >>>>> 1 + . >>>>> . >>>>> . >>>>> >>>>> table >>>>> _1 1 1r12 1r60 1r140 1r252 1r396 >>>>> 1 1r2 1 1 1 1 1 >>>>> 1 3 19r7 193r71 2721r1001 49171r18089 1084483r398959 >>>>> >>>>> >>>>> You must ignore the _1 in the upper left corner. You see how the first >>>> row >>>>> identifies numerators and the second row numbers on the "diagonal" of >> the >>>>> continued fraction. >>>>> >>>>> >>>>> The third row gives the "convergents", results of terminating the >>>> continued >>>>> fraction at a diagonal number. The first four convergents are >>>>> >>>>> 1 , (1 + 1 % 1r2) , (1 + 1 % 1r2 + 1r12 % 1) , (1 + 1 % 1r2 + 1r12 % >> 1 + >>>>> 1r60 % 1) >>>>> >>>>> >>>>> The convergents of this continued fraction approximate the number e >> =: >>>> ^ 1 >>>>> . >>>>> >>>>> 2 * 0.5 * {: table >>>>> 1 3 2.714285714 2.718309859 2.718281718 2.718281829 2.718281828 >>>>> >>>>> >>>>> Now, how would you write verb cv which provides the third row of the >>>> table >>>>> given the first two? >>>>> >>>>> 2 {. table >>>>> _1 1 1r12 1r60 1r140 1r252 1r396 >>>>> 1 1r2 1 1 1 1 1 >>>>> >>>>> cv 2 {. table >>>>> 1 3 19r7 193r71 2721r1001 49171r18089 1084483r398959 >>>>> >>>>> >>>>> --Kip Murray >>>>> >>>>> >>>>> >>>>> -- >>>>> Sent from Gmail Mobile >>>>> ---------------------------------------------------------------------- >>>>> For information about J forums see >> http://www.jsoftware.com/forums.htm >>>> ---------------------------------------------------------------------- >>>> For information about J forums see http://www.jsoftware.com/forums.htm >>> >>> >>> >>> -- >>> Sent from Gmail Mobile >>> ---------------------------------------------------------------------- >>> For information about J forums see http://www.jsoftware.com/forums.htm >> ---------------------------------------------------------------------- >> For information about J forums see http://www.jsoftware.com/forums.htm > > > > -- > Sent from Gmail Mobile > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm
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