Question

In a chess board if I put one coin on the first square of the chess board to coin for the next square 4 coins for the next 8 for the next and so on for all 64 squares with each each square having double number of coins as a square before. Find the total number of kinds I will get.

Answer 1

To find the total number of coins you will have, we can calculate the sum of a geometric series. In this case, the first term is 1 (the number of coins on the first square) and the common ratio is 2 (each square has double the number of coins as the previous square).

The formula to calculate the sum of a geometric series is:

S = a * (r^n - 1) / (r - 1)

Where:
S = sum of the series
a = first term
r = common ratio
n = number of terms

In this case, a = 1, r = 2, and n = 64 (since there are 64 squares on a chessboard).

Plugging in these values into the formula, we get:

S = 1 * (2^64 - 1) / (2 - 1)

Simplifying the equation:

S = (2^64 - 1)

Calculating this value, we find that the total number of coins you will have is:

S = 18,446,744,073,709,551,615

Therefore, you will have a total of 18,446,744,073,709,551,615 coins.