1 = 0

Proof:
1 = 1 + (-1 + 1) + (-1 + 1) + (-1 + 1) + ....
  = (1 + -1) + (1 + -1) + (1 + -1) + (1 + -1) + ......
  = 0

kekekeke

Wikipedia says it is non-convergent so it must be true. (http://en.wikipedia.org/wiki/Grandi%27s_series)

In modern mathematics, the sum of an infinite series is defined to be equal to the limit of the sequence of its "partial sums", if it exists. The sequence of partial sums of Grandi's series is (1, 0, 1, 0, …) - it clearly does not "approach" any number ( although it does have two accumulation points - 0 and 1 ). Therefore, Grandi's series is non-convergent, or oscillating.