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A woman labels the squares of a very large chessboard 1 through 64. On each square k, the woman puts 2^k grains of rice. How many more grains of rice are placed on the 10th square than on the first 9 squares combined?

 Apr 8, 2022
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This is not that difficult by finding and adding the individual terms; however, you can use the formula for the

sum of a finite geometric series:     Sum  =  a1 · (1 - rn) / (1 - r)

where  a1 = 2  and  r = 2:                Sum  =  2 · (1 - 29) / (1 - 2)  =  1022

 

 Compare this to:  210  =  1024

 Apr 8, 2022

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