Sequences & Series

A king offers a wise advisor any reward. The advisor asks for one grain of wheat on the first square of a chessboard, two on the second, four on the third, doubling each square. The king laughs at such a modest request — until the royal granary runs dry. By the 64th square the total exceeds a thousand years of global wheat harvest. That's a GEOMETRIC series, and its sum explodes because each term MULTIPLIES by a constant ratio. Sequences are lists; series are their sums — and the two great families, arithmetic (add a constant) and geometric (multiply a constant), have elegant formulas that total them instantly.