Wolfram Research, Inc.

Problem 3

What is 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.

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.