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Gerson W. Barbosa · (This post was last modified: 08-09-2022 11:08 AM by Gerson W. Barbosa.)

(08-07-2022 07:55 AM)Thomas Klemm Wrote: We can calculate a numerical approximation using Bernoulli's Method with the following program for the HP-42S:

Code:

00 { 4-Byte Prgm } 01 ENTER 02 RCL+ ST T 03 END

Initialise the stack with:

CLST
1

And then hit repeatedly the R/S key:

R/S
R/S
R/S
…

This will do for the 12 digits in the display:

67
ENTER
X↑2
1/X
+
11
1/X
Y↑X

Or, for more digits,

(67 + 1/(67^2 + 2/(67 + 3/(2×67^2 + 11/(3×67)))))^(1/11)
= 1.46557123187676802665673122475

The latter should take up more steps than the exact expression, though.

P.S.:

300766 ENTER 33 1/X Y↑X is shorter for 12 digits and the approximation is slightly better.