I want to prove the following identity: . I can see this seems to be true tabulating the values of and thus:
And now, instead of adding over the rows, I can add over the columns. However, I cant prove the identity. Any help will be welcome. Regards.
Note: the table lends itself to the proof. But I'd like to prove the identity by, for instance, manipulating the limits and indexes of the sums or, not so nice, by induction.