A sequencesuperconverges to 0 if, when the are written in base 2, then each number starts with
zeroes. For example, the following sequence is superconverging to 0.
In this case it is easy to see that the number of binary 0's doubles each .
A sequence superconverges to if superconverges to 0, and a sequence is said to be superconvergent if there exists a to which the sequence superconverges.
![\begin{displaymath}\begin{array}{clcl} x_{n+1}&=x_n^2 & (x_n)_{10} & (x_n)_2\\ [... ...1.5pt] x_4 &= & \frac{1}{65536} & .0000000000000001 \end{array}\end{displaymath}](http://images.planetmath.org:8080/cache/objects/793/l2h/img5.png "\begin{displaymath}\begin{array}{clcl} x_{n+1}&=x_n^2 & (x_n)_{10} & (x_n)_2\\ [... ...1.5pt] x_4 &= & \frac{1}{65536} & .0000000000000001 \end{array}\end{displaymath}")
