Company
Mathematica Solutions to the ISSAC '97 Systems Challenge

Wolfram Research, Inc.


Problem 3

What is [Graphics:ISSACChallengegr43.gif]to 14 significant digits?

Result
21.19324037771154...


Method: Use a built-in function.

The most natural approach gives the first seven digits but also generates messages that tell us that the tail estimate failed.

[Graphics:ISSACChallengegr7.gif][Graphics:ISSACChallengegr44.gif]
[Graphics:ISSACChallengegr7.gif][Graphics:ISSACChallengegr45.gif]
[Graphics:ISSACChallengegr7.gif][Graphics:ISSACChallengegr46.gif]
[Graphics:ISSACChallengegr7.gif][Graphics:ISSACChallengegr47.gif]

To guarantee 14 digits we use bignum arithmetic (as recommended in the error message). Because we know that the sum converges, we don't need to verify the convergence numerically.

[Graphics:ISSACChallengegr7.gif][Graphics:ISSACChallengegr48.gif]
[Graphics:ISSACChallengegr7.gif][Graphics:ISSACChallengegr49.gif]