- #1

Jehannum

- 102

- 26

$$\frac a b = \frac a {(b-1)} - \frac a {{(b-1)}^2} + \frac a {{(b-1)}^3} - \frac a {{(b-1)}^4} + ~...$$

I have done a bit of work on it myself, and have tried to research similar series. It seems to lead to some interesting results. For example, when a = 1 and b = 2 it doesn't work because you get 1 - 1 + 1 - 1 + 1 ... but it's interesting that the Cesaro sum of this series is 1/2.

Can anyone provide links or information on anything relevant?