In ancient times, there was a wise minister in a kingdom. He invented chess and presented it to the king. The king has been fascinated with chess ever since. In order to express his gratitude to the minister, the king promised to meet a request of the minister. The minister said, "Just put some rice grains on this chessboard. Put 1 grain rice in 1 grid, put 2 grains of rice in the second grid, put 4 grains of rice in the third grid, then put 8 grains of rice, 16 grains of rice, 32 grains of rice ... until 64 grids. " "You are so stupid, do you want this millet?" The king smiled. The minister said, "I'm afraid there isn't that much rice in your treasury!" " "Are there really not so many kings?

Now let's help the king figure out how many grains of rice the minister wants and whether there is so much rice in the king's treasury.

The chessboard has 64 squares. If you press 1, 2, 4, 8, 16, 32, ... that is,,,, ... put it on the chessboard. You should put so many rice grains in the 64th square, so you should put so many rice grains in the 64th square.

Here,,,,,,,,,, forms a geometric series with 2 as the common ratio and 1 as the prime number, and the total number of rice grains required by the minister is the sum of this geometric series. The sum of these 64 numbers can be obtained by the summation formula of equal ratio series:

==

This is a considerable number, because

= 1024× 1024× 1024× 1024× 1024× 1024× 16

Although this is not an accurate figure, it is not difficult to see how big the result is from this formula. Will there be so much rice in the king's treasury? Needless to say, everyone probably already knows the answer.

In addition: here y=(n is an independent variable, n = 0, 1, 2, 3, ..., 63) is an exponential function, and it is a monotonically increasing function, so the integer value will increase with the increase of n, and there is a mathematical saying called "exponential explosion", which refers to an increasing exponential function. When the index of the increasing exponential function is larger and larger, the image of the exponential function will increase faster and faster, and the image will rise like a straight line. So this is a very big number.