Summing an infinite series paradox


0 = 1 - 1 + 2 - 2 + 3 - 3 + 4 - 4                                                     L1
The above is fine, but what about the infinite version:

0 = 1 - 1 + 2 - 2 + 3 - 3 + 4 - 4 + ...                                              L2
There is nothing wrong with writing out infinitely many terms like this.

Yet we can re-arrange it to give
0 = 1 + ( -1 + 2 ) + ( -2 + 3 ) + ( -3 + 4 ) + ( -4 + 5 ) + ...             L3
   = 1 + 1 + 1 + 1 + ...
   = infinity

Solution


Home          IFAQ Home          IFAQ           Qs           Etc           Forum           Aphorisms           Puzzles           Humour           Poetry      Fiction           About