Question

A King in ancient times agreed to reward the inventor of chess with one grain of wheat on the first of the 64 squares of a chess board. On the second square the King would place two grains of​ wheat, on the third​ square, four grains of​ wheat, and on the fourth square eight grains of wheat. If the amount of wheat is doubled in this way on each of the remaining​ squares, how many grains of wheat should be placed on square 25​? Also find the total number of grains of wheat on the board at this time and their total weight in pounds.​ (Assume that each grain of wheat weighs​ 1/7000 pound.)

Answer 1

That's 2635249153387078 pounds or 1317624576693.5 tons

Explanation:

The series is 2^(n-1) where n=1,2,3,4,...,62,63,64

We can adjust the index and write it as 2^n where n=0,1,2,3,4,...,61,62,63

The sum of the geometric series is:

a1 * (1 - r^n)

------------------

1-r

where r is the common ratio in this case 2,

a1 is the first term, in this case 1,

and n is the number of term, in this case 64

1 * (1 - 2^64)

---------------- = 18446744073709551615

1 - 2

Dividing that by 7000

That's 2635249153387078 pounds or 1317624576693.5 tons

Hope this helped!