The legend of the chessboard

History — The legend of the chessboard

It is said that the inventor of chess, received in audience by the sovereign, asked as a reward for one grain of wheat on the first square, two on the second, four on the third, and so on doubling for all $64$ squares. It is a GP with $a_1 = 1$ and $q = 2$: $S_{64} = \frac{2^{64}-1}{2-1} = 2^{64}-1 \approx 1{,}8\cdot 10^{19}\ \text{chicchi}.$ That is more wheat than has ever been produced in the whole history of humanity.

The legend is didactically perfect: in a few steps it shows why geometric growth is qualitatively different from arithmetic growth.

Links

Topics: Sequences
Concepts: Geometric progression
Methods: Sum of a geometric progression