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

Answer:

He will get $2^{64}-1\:coins$

Step-by-step explanation:

No. of coins in square 1= 1

No. of coins in square 2= 2(1)=2

No. of coins in square 3= 2(2)=2²

No. of coins in square 4= 2(2²)=2³

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No.of coins in square 64 $= 2^{63}$

Clearly 1, 2, 2 ², 2³,...........forms a G.P

Total no. of coins he will get

=sum of first 64 terms of the G.P

$=\frac{a(r^n-1)}{r-1}$

$=\frac{1(2^{64}-1)}{2-1}$

$=2^{64}-1\:coins$