An observation. I'm also vouching for something for an unique realtion between Grandi's Series and the value 1/2. Beside those videos in Numberphile, I stumbled upon the following Taylor Series of 1/(1-x). Which then can let have the following series for x in (0,2):
1/x = 1 + (1-x) + (1-x)^2 + (1-x)^3 + (1-x)^4 + ...
Of course, as it is definied, x=2 is not permissible. Yet when we take the limit of x as it approaches 2, you get something very similar to Grandi's Series. I'm not quite sure if we definitely say
1/2 =
But I did find this quite interesting.
