Geometric Progression

Geometrical progressions give rise to numbers which can be extremely large. One of the large numbers arising from geometric progressions is the number of grains of corn that can be placed on a chessboard.

According to legend, a man named Sessa invented the game of chess and presented it to the king. The king was so pleased that he promised to reward Sessa with whatever he asked for. Sessa asked for a grain of corn for first of 64 squares of his chessboard, 2 grains for second, 4 for third, 8 for fourth and so on, doubling the number of grains in each square up to last.

The king agreed to Sessa’s request without hesitation. Sessa showed the king that he could never grant his request no matter how rich the king was.

The number of grains of corn worked out to be very large, 264-1 (2 to the power 64 minus 1) which is equal to 18 446 744 073 709 551 615 I repeat 18 446 744 073 709 551 615. It will take several centuries for the world to produce this much grain of corn.

I am also giving the proof

The arrangement forms a geometric progression with Starting number 1 and common ratio 2. And according to Sessa total number of term is 64. So sum of all 64 terms is –