Motivation for Ramanujan's mysterious $\pi$ formula The following formula for $\pi$ was discovered by Ramanujan:
$$\frac1{\pi} = \frac{2\sqrt{2}}{9801} \sum_{k=0}^\infty \frac{(4k)!(1103+26390k)}{(k!)^4 396^{4k}}\!$$
Does anyone know how it works, or what the motivation for it is?

The explanation for the existence of this series is given here. Search for the phrase
"The general form of the series is" to locate it. The series cited in the question appears immediately before the explanation.
