Natural logarithm of 2 [HP-15C/HP-42S/Free42 & others]

[Thomas Klemm]

This program for the HP-42S uses formula (19):

\(
\begin{align}
\ln 2= \sum_{k=1}^{\infty} \frac{1}{k \cdot 2^k}
\end{align}
\)

Code:

00 { 14-Byte Prgm }
01 0
02▸LBL 00
03 RCL ST Y
04 1/X
05 +
06 2
07 ÷
08 DSE ST Y
09 GTO 00
10 END

37
R/S

0.693147180559758517350355291780403
0.6931471805599453094172321214581766


105
R/S

0.6931471805599453094172321214581765
0.6931471805599453094172321214581766


I have no idea how long it takes on a real HP-42S.