Question

In a chessboard if I put one coin for 1st square of chess board, two coins for next
square, four coins for the next , eight for the nest and so on for all 64 squares
with each square having double the number of coins as the square before . Find
the total number of coins I will get.
Please also tell the logic

Answer 1

Answer:

2⁶⁴ - 1

18446744073709551615

Step-by-step explanation:

In a chessboard if I put one coin for 1st square of chess board, two coins for next  

square, four coins for the next , eight for the nest and so on for all 64 squares  

with each square having double the number of coins as the square before

There are total 64 boxes in a chess

1st box = 1

2nd box = 2 * 1 = 2¹

3rd box = 2 * 2¹ = 2²

4th Box = 2 * 2² = 2³

64th Box = 2⁶³

1 + 2 + 2² + 2³ + ...................................................+ 2⁶² + 2⁶³

This is an GP

where a = 1  r = 2  n = 64

Sum of a GP = a* (rⁿ - 1) /(r - 1)

= 1 * (2⁶⁴ - 1) /(2 - 1)

= 2⁶⁴ - 1

= 18446744073709551616 - 1

= 18446744073709551615