[VA] SRC#002- Almost integers and other beasties

[Valentin Albillo]

 
Hi again,
      
Dealing with some search theory, I recently came across this short expression:

\[ \frac{1}{12}+\frac{\Pi^2}{6Ln^2(2)}+ \frac{2}{Ln(2)} \sum_{k=1}^\infty \frac{(-1)^k}{k(2^k-1)} \]
which this straightforward HP-71B program (a command-line expression would work as well) quickly evaluates to the apparently exact integer value 1:

      1    DESTROY ALL @ V=0 @ FOR K=1 TO 40 @ V=V+(-1)^K/K/(2^K-1) @ NEXT K
      2    V=V*2/LN(2)+1/12+PI^2/6/LN(2)^2 @ DISP V

      >RUN
            1

But it's not !
See if you can get the actual, more accurate almost-integer value with your HP. It certainly qualifies as a most amazing almost-integer one !

V.
.