How do you compute the first two rows? Thanks,
-- Raul On Saturday, March 12, 2016, Kip Murray <[email protected]> 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
