What do you mean Detmer. The series are both the same. Just the () have been placed in different places to emphasize what numbers you should add together first.

Since this forum has already come to realise that 0.9999... = 1 time to introduce new ground breaking results to you.

1 = 1 + (−1 + 1) + (−1 + 1) + ... = 1 − 1 + 1 − 1 + ... = (1 − 1) + (1 − 1) + ... = 0