Suppose we have a chessboard (contains 64 quods). In the first quod we put 0.01 ¤ (1 cents) in the
second squod double the previous one and continue this process until the 64th square, how much money we have
put on the board?
Choose between:
a) (263 -1)¤
b) 0.01 . (263 -1)¤
c) (264 -1)¤
d) 0.01 . (264 -1)¤
1 + 2 + 4 + 16 .....
geometric series with 64 terms
1 + 1(2) + 1(2)^2 + 1(2)^3 + .... 1(2)^63
Sum = 1 (1-2^64)/(1-2) = 2^64 – 1 = 1.84467 *10^19 – 1
All in cents so in dollars
1.84467*10^17 - .01
thank you...it is the d..
To find out how much money is put on the chessboard, we can use the concept of geometric progression. Each square on the chessboard will have double the amount of money as the previous square.
The amount of money on each square can be represented by the formula: 0.01 * (2^(n-1)), where n represents the number of the square.
To find the total amount of money on the chessboard, we need to sum up the amounts on each square from 1 to 64.
The formula for summing up a geometric progression is: Sn = a * ((r^n) - 1) / (r - 1), where Sn is the sum of the series, a is the first term, r is the common ratio, and n is the number of terms.
In this case, the first term (a) is 0.01¤, the common ratio (r) is 2, and the number of terms (n) is 64.
Substituting these values into the formula, we can calculate the total amount of money on the chessboard:
S64 = 0.01 * ((2^64) - 1) / (2 - 1)
S64 = 0.01 * (2^64 - 1)
S64 ≈ 183,251,937,939,063.98¤
Therefore, the correct answer is c) (264 - 1)¤