What is 1 + 1 - 1 + 1 - 1 + 1 (continuous)?

Geno....doesn't this come from the Indian mathematician, Ramanujan ???

I seem to remember [from Calculus class]   that he showed  that the same series could have different sums according to the arrangement of the series........

It has no "answer".

If the terms are arranged as: 1 + (1 - 1) + (1 - 1) + (1 - 1) + ...

          then the answer will be 1 + 0 + 0 + 0 + ...  =  1.

However, if the terms are arranged as:  1 + 1 + (-1 + 1) + (-1 + 1) + (-1 + 1) + ...

        then the answer will b2 2 + 0 + 0 + 0 + ...  =  2.

So, there is no single "answer".

(You might like to see if you can rearrange the terms to get other answers ...)