  It is mathematical folklore that 1 + 2 + 3 + 4 + ... = --1/12. This result is
usually achieved using elaborate analytical methods, such as zeta function
regularization or Ramanujan summation. However, in its notebooks, Ramanujan has
also provided a very simple derivation which relied instead on algebraic
manipulations. Recently, a video from Numberphile has presented a similar
derivation of the result (provoking lots of discussions and debates about the
meaning of such an equality). But this derivation, simple as it is, is usually
considered as less rigorous than those using more elaborate analytical methods.
However, this derivation is indeed perfectly rigourous, and in this article, we
will define a general algebraic construction which we will use as a framework
for expressing this derivation and, more generally, for providing a new
summation method.
