Solution to rice and chessboard problem?

Question

There is an old math problem about the man who invented chess. See, the king at the time loved the game so much, he told the inventor to name whatever he wanted for compensation. The inventor asked for the king to place one grain of wheat on the first square of the chessboard. And in the second square, double the grains of wheat (so two), and in the third, double what came before (so four grains of wheat). And the inventor said as long as the king kept up this doubling for 94 squares on the board, he'd be satisfies. The king laughed it off and said, "Sure." How many grains of wheat is this?

Answer 1

There are only 64 squares on a chess board, so 2⁶³, since the first square is 2⁰, = 92,233,720,368,554,775,808 grains of wheat.

Answer 2

This is the sum of a geometric series.

a₁ = 1, r = 2, n = 94

 

S_n = a₁(1 - rⁿ) / (1 - r)

 

Can you substitute and calculate?