Respuesta :
This is just like the rice chessboard problem! To quickly get the answer, we can simply do (2^64)-1.
Take a look at the following:
1+2+4+8=15=2^4-1
1+2+4+8+16=31=2^5-1
There's that rule involved, and we can simply use 2^64-1 instead of adding too many numbers.
Hope this helped!
Total number of pennies on the chessboard is equals to [tex]2^{64} -1[/tex].
Total number of squares on the chessboard = 64
What is pattern?
" Pattern is defined as the numbers are arranged in such a way that it follow certain rule or formula."
According to the question,
Number of pennies in first square = 1
Number of pennies in second square = 2
Number of pennies in third square = 4
Condition given,
Doubling the number of pennies on each subsequent square.
Calculate pattern follow as per given condition we have,
Total Number of pennies in first square = 1
= [tex]2^{1} -1[/tex]
Total Number of pennies till second square = 1 + 2
= [tex]2^{2} -1[/tex]
Total Number of pennies till third square = 1+ 2 + 4
= [tex]2^{3} -1[/tex]
Total Number of pennies till fourth square = 1+ 2 + 4 +8
= [tex]2^{4} -1[/tex]
Total number of squares on the chessboard = 64
Therefore, as per the pattern follow on each subsequent square we get,
Total number of pennies till 64th squares chessboard = [tex]2^{64} -1[/tex]
Hence, total number of pennies on the chessboard is equals to [tex]2^{64} -1[/tex].
Total number of squares on the chessboard = 64.
Learn more about pattern here
https://brainly.com/question/14720576
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