April 2007 UTC Rosa I think this might help In mathematics if you can define a set of rules that s consistent with itself then you can work with those rules According to the definition of sum and equals that most of us are used to it makes no sense to say that 1 2 3 4 equals anything However there are other somewhat more generous ways of defining sum and equals that don t contradict our ordinary finite arithmetic but which produce some additional surprising results with infinite sums There are definitions and sets of rules under which experssions like the one in this article can make sense and add up to a particular number Within those rulesets the sum is oddly enough 1 4 I think one good way to see how that could possibly work is to consider this if you take the series 1 2 3 4 and write it down 4 times in just the right way you can see how all the positive terms and all the negative terms cancel out except for one of the initial 1 s Thus four copies of the series add up to 1 so each one must equal 1 4 01 30 19