Euler's Finite Difference Transformation

A transformation for the acceleration of the convergence of slowly converging Alternating Series,

$$\sum_{k=0}^\infty (-1)^k a_k = \sum_{n=0}^\infty {\Delta^k a_0\over 2^{n+1}}.$$

References

Iyanaga, S. and Kawada, Y. (Eds.). Encyclopedic Dictionary of Mathematics. Cambridge, MA: MIT Press, p. 1163, 1980.