Grandi's series

In mathematics, the infinite series 1 − 1 + 1 − 1 + ⋯ is a divergent series, meaning that the sequence of partial sums of the series does not converge. Although it is divergent, it can be manipulated to yield a number of mathematically interesting results. In particular, various summation methods (techniques for assigning numerical values even to a divergent series) assign this series the value ⁠1/2⁠.

The series, which can also be written as $${\displaystyle \sum _{n=0}^{\infty }(-1)^{n},}$$ is sometimes called Grandi's series, after Italian mathematician, philosopher, and priest Guido Grandi, who gave a memorable treatment of the series in 1703.